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3 years ago

How to add rational expressions.

1 answer:

8 0

First, some general rules to remember:

Rational expressions (fractions) can only be added or subtracted if they have a common denominator.
The numerator and denominator of a fraction may be multiplied by the same quantity. This will result in a fraction that is equivalent to the original fraction.
For a fractional answer to be in final form, the fraction must be reduced to lowest terms.
Adding or subtracting rational expressions is a four-step process:

Write all fractions as equivalent fractions with a common denominator.
Combine the fractions as a single fraction that has the common denominator.
Simplify the expression in the top of the fraction.
Reduce the fraction to lowest terms.
To see this process, we'll look at some examples.

Example 1

Step 1: To find a common denominator, start by factoring the denominators of both fractions.

The least common denominator of these two fractions is 2(x+6)(x-6).

Looking at the first fraction, we can see that the factor missing from its denominator is (x-6). In the next step, we'll multiply the top and bottom of the first fraction by (x-6).

Looking at the second fraction, we can see that the factor missing from its denominator is 2. In the next step, we'll multiply the top and bottom of the second fraction by 2.

Step 2: Now that the fractions have the same denominators, we'll create one combined fraction by adding the two fractions together:

Step 3: We'll simplify the top of the fraction. Notice that we are only simplifying the top of the fraction; the bottom of the fraction remains unchanged.

Step 4: Now we'll reduce the fraction to lowest terms

Example 2

Step 1: To find a common denominator, start by factoring the denominators of both fractions.

The least common denominator of these two fractions is (x+4)(x+1)(x+3).

Looking at the first fraction, we can see that the factor missing from its denominator is (x+3). In the next step, we'll multiply the top and bottom of the first fraction by (x+3).

Looking at the first fraction, we can see that the factor missing from its denominator is (x+4). In the next step, we'll multiply the top and bottom of the first fraction by (x+4).

Step 2: Now that the fractions have the same denominators, we'll create one combined fraction by adding the two fractions together:

Step 3: We'll simplify the top of the fraction. Notice that we are only simplifying the top of the fraction; the bottom of the fraction remains unchanged.

Step 4: Now we'll reduce the fraction to lowest terms

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I am a fraction whose Numerator and denominator are both prime numbers less than 20. If you were to increase each term by 1‚ I w

11Alexandr11 [23.1K]

Answer:

$\frac{2}{5}$ .

Step-by-step explanation:

Let the unknown fraction be $\frac{x}{y}$ ,

where, x and y both are prime numbers less than 20.

Now, it is given that adding 1 to both numerator and denominator will make the fraction $\frac{1}{2}$ .

Thus,

$\frac{x+1}{y+1}$ = $\frac{1}{2}$

2(x + 1) = y + 1

2x + 2 = y + 1

2x + 1 = y.

Clearly if x will be any odd number , two times x will be odd and adding 1 to it will result in even number and y should be even number , which is not possible as only even prime is 2.

Thus , x should be the even prime which is 2.

And y will be 5.

Thus the required fraction is $\frac{2}{5}$ .

6 0

3 years ago

A refreshment stand makes 2 large servings of frozen yogurt from 3 pints. Add the line to the graph and write the equation.

nignag [31]

Answer:

$y=(2/3)x$

The graph in the attached figure

Step-by-step explanation:

Let

x-----> the number of pints

y----> the number of servings

For x=3 pints, y=2 servings

This is a proportional variation

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

The linear equation is equal to

$y=(2/3)x$

The graph in the attached figure

4 0

4 years ago

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A report on consumer financial literacy summarized data from a representative sample of 1,663 adult Americans. Based on data fro

Tom [10]

Answer:

a) 95% Confidence interval = (0.536, 0.584)

This means that we are 95% confident that between 53.6% and 58.4% of Americans would give themselves grade of A or B on their financial knowledge of personal finance.

b) The result of the 95% confidence interval agrees with the claim that majority of Americans would give themselves a grade of A or B on their financial knowledge of personal finance because the interval obtained for possible values that the population proportion of Americans that would give themselves a grade of A or B on their financial knowledge of personal finance lies completely on the side that is greater than a proportion of 0.50 which indicates that truly, majority of Americans would give themselves a grade of A or B on their financial knowledge of personal finance.

Step-by-step explanation:

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion = proportion of Americans in the sample that would give themselves grade of A or B on their financial knowledge of personal finance = p = (934/1663) = 0.56

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 95% confidence interval for sample size of 1663 is obtained from the z-tables as the sample size is large enough for the sample properties to approximate the population properties.

Critical value = 1.960 (from the z-tables)

Standard error of the mean = σₓ = √[p(1-p)/n]

p = 0.56

n = sample size = 1663

σₓ = √[0.56×0.44/1663] = 0.0121723457 = 0.01217

95% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.56 ± (1.96 × 0.01217)

CI = 0.56 ± 0.0238532

95% CI = (0.5361468, 0.5838532)

95% Confidence interval = (0.536, 0.584)

Hope this Helps!!!

5 0

4 years ago

jamal works in a city and sometimes takes a taxi to work. the taxicab charge $1.50 for the first 1/5 miles and $0.25 for each ad

Llana [10]

One and one-fifth mile

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3 years ago

Complete the table for the given rule.<br> Rule: y = x + 8<br> (there’s and image with the problem.)

borishaifa [10]

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4 0

3 years ago

Read 2 more answers