I NEED HELP OMG SOMEONE PLS HELP ME IM FAILING AND MY PARENTS ARE BIG MAD

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

4 years ago

Read 2 more answers

Simplify. (3/4√15) (16√5) A60√5 B 60√3 C 50√3

Andrew [12]

Answer: OPTION B

Step-by-step explanation:

You have the following expresion:

$(\frac{3}{4}\sqrt{15})(16\sqrt{5})$

Mulitply them, then:

$=12\sqrt{75}$

Now, descompose the number inside the square root into it primes factor to simplify the expression:

75=5*5*3=5²*3

Substitute:

$=12\sqrt{5^2*3}$

Simplify. Then, you obtain:

$=12*5\sqrt{3}$

$=60\sqrt{3}$

6 0

3 years ago

Which equation represents the same line points as the table

Anettt [7]

Answer:

y=-x,A

Step-by-step explanation:

When we input -5 in for x, we get 5

When we input 7 in for x, we get -7

4 0

3 years ago

The perimeter of a rectangular field is 314 m.

Ksivusya [100]

Answer:

85m

Step-by-step explanation:

Perimeter of a rectangle = 2(l+b)

b=72m, l=?

perimeter =314m

314=2(l+72)

314/2= l+72

157=l+72

l=157-72

l=85m

3 0

2 years ago

Which of the following is not a property of a chi-square distribution?

laiz [17]

Answer:

c) Is not a property (hence (d) is not either)

Step-by-step explanation:

Remember that the chi square distribution with k degrees of freedom has this formula

$\chi_k^2 = \matchal{N}_1^2 + \matchal{N}_2^2 + ... + \, \matchal{N}_{k-1}^2 + \matchal{N}_k^2$

Where N₁ , N₂m .... $N_k$ are independent random variables with standard normal distribution. Since it is a sum of squares, then the chi square distribution cant take negative values, thus (c) is not true as property. Therefore, (d) cant be true either.

Since the chi square is a sum of squares of a symmetrical random variable, it is skewed to the right (values with big absolute value, either positive or negative, will represent a big weight for the graph that is not compensated with values near 0). This shows that (a) is true

The more degrees of freedom the chi square has, the less skewed to the right it is, up to the point of being almost symmetrical for high values of k. In fact, the Central Limit Theorem states that a chi sqare with n degrees of freedom, with n big, will have a distribution approximate to a Normal distribution, therefore, it is not very skewed for high values of n. As a conclusion, the shape of the distribution changes when the degrees of freedom increase, because the distribution is more symmetrical the higher the degrees of freedom are. Thus, (b) is true.

6 0

3 years ago