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Mama L [17]
3 years ago
15

Please Help me! 20 points

Mathematics
1 answer:
malfutka [58]3 years ago
6 0

Answer:

-9/4 ÷ (-2/3)

Step-by-step explanation:

-(2 1/4) ➡ -9/4

-2/3 ➡ (again a reciprocal needed) -3/2 since we need the result to be positive both expression should remain negative so the answer is -9/4 ÷ -2/3

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Simplify (x + 2/ x^2 + 2x -3) / (x + 2/x^2 - x)
rjkz [21]

Answer:

The simplest form is x/(x + 3)

Step-by-step explanation:

* To simplify the rational Expression lets revise the factorization

  of the quadratic expression

*  To factor a quadratic in the form x² ± bx ± c:

- First look at the c term  

# If the c term is a positive number, and its factors are r and s they

  will have the same sign and their sum is b.

#  If the c term is a negative number, then either r or s will be negative

   but not both and their difference is b.

- Second look at the b term.  

# If the c term is positive and the b term is positive, then both r and

  s are positive.  

Ex: x² + 5x + 6 = (x + 3)(x + 2)  

# If the c term is positive and the b term is negative, then both r and s

  are negative.  

Ex:  x² - 5x + 6 = (x -3)(x - 2)

# If the c term is negative and the b term is positive, then the factor

  that is positive will have the greater absolute value. That is, if

  |r| > |s|, then r is positive and s is negative.  

Ex: x² + 5x - 6 = (x + 6)(x - 1)

# If the c term is negative and the b term is negative, then the factor

  that is negative will have the greater absolute value. That is, if

  |r| > |s|, then r is negative and s is positive.

Ex: x² - 5x - 6 = (x - 6)(x + 1)

* Now lets solve the problem

- We have two fractions over each other

- Lets simplify the numerator

∵ The numerator is \frac{x+2}{x^{2}+2x-3}

- Factorize its denominator

∵  The denominator = x² + 2x - 3

- The last term is negative then the two brackets have different signs

∵ 3 = 3 × 1

∵ 3 - 1 = 2

∵ The middle term is +ve

∴ -3 = 3 × -1 ⇒ the greatest is +ve

∴ x² + 2x - 3 = (x + 3)(x - 1)

∴ The numerator = \frac{(x+2)}{(x+3)(x-2)}

- Lets simplify the denominator

∵ The denominator is \frac{x+2}{x^{2}-x}

- Factorize its denominator

∵  The denominator = x² - 2x

- Take x as a common factor and divide each term by x

∵ x² ÷ x = x

∵ -x ÷ x = -1

∴ x² - 2x = x(x - 1)

∴ The denominator = \frac{(x+2)}{x(x-1)}

* Now lets write the fraction as a division

∴ The fraction = \frac{x+2}{(x+3)(x-1)} ÷ \frac{x+2}{x(x-1)}

- Change the sign of division and reverse the fraction after it

∴ The fraction = \frac{(x+2)}{(x+3)(x-1)}*\frac{x(x-1)}{(x+2)}

* Now we can cancel the bracket (x + 2) up with same bracket down

 and cancel bracket (x - 1) up with same bracket down

∴ The simplest form = \frac{x}{x+3}

5 0
3 years ago
Read 2 more answers
Light travels at a speed of about 186,000 miles per second. How far does light travel in 5 seconds? Use repeated addition to sol
aleksklad [387]
186,000+186,000+186,000+186,000+186,000=186,000*5=

930,000 miles in 5 seconds. Good luck my friend!
7 0
2 years ago
Greg plowed for 2.5 hours in the morning, 1 hour and 15 minutes in the afternoon, and 1 hour and 30 minutes in the evening. How
HACTEHA [7]

Answer:

Five hours and fifteen minutes.

Step-by-step explanation:

You add all these together and it gets five hours and fifteen minutes.

6 0
3 years ago
Help me on this one please​
soldi70 [24.7K]

Answer:

615.8

Step-by-step explanation:

Circle area = π * r² = π * 196 [mcm²] ≈ 615.8 [cm²]

7 0
1 year ago
Read 2 more answers
If f (x) = 5x + 4 then for what value of x will f(x) equal -11?​
uysha [10]

Answer:

-3

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
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