Simplify 7/(x^2+2x-35)-(5x)/(x+7)

$\frac{7}{x^{2} + 2 x - 35} - \frac{5 x}{x + 7}$

Factor $x^{2} + 2 x - 35$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 35$ and whose sum is $2$ .

$- 5, 7$

Write the factored form using these integers.

$\frac{7}{(x - 5) (x + 7)} - \frac{5 x}{x + 7}$

To write $- \frac{5 x}{x + 7}$ as a fraction with a common denominator, multiply by $\frac{x - 5}{x - 5}$ .

$\frac{7}{(x - 5) (x + 7)} - \frac{5 x}{x + 7} \cdot \frac{x - 5}{x - 5}$

Write each expression with a common denominator of $(x - 5) (x + 7)$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5 x}{x + 7}$ by $\frac{x - 5}{x - 5}$ .

$\frac{7}{(x - 5) (x + 7)} - \frac{5 x (x - 5)}{(x + 7) (x - 5)}$

Reorder the factors of $(x - 5) (x + 7)$ .

$\frac{7}{(x + 7) (x - 5)} - \frac{5 x (x - 5)}{(x + 7) (x - 5)}$

Combine the numerators over the common denominator.

$\frac{7 - 5 x (x - 5)}{(x + 7) (x - 5)}$

Simplify the numerator.

Apply the distributive property.

$\frac{7 - 5 x \cdot x - 5 x \cdot - 5}{(x + 7) (x - 5)}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$\frac{7 - 5 (x \cdot x) - 5 x \cdot - 5}{(x + 7) (x - 5)}$

Multiply $x$ by $x$ .

$\frac{7 - 5 x^{2} - 5 x \cdot - 5}{(x + 7) (x - 5)}$

Multiply $- 5$ by $- 5$ .

$\frac{7 - 5 x^{2} + 25 x}{(x + 7) (x - 5)}$

Reorder terms.

$\frac{- 5 x^{2} + 25 x + 7}{(x + 7) (x - 5)}$

Simplify with factoring out.

Factor $- 1$ out of $- 5 x^{2}$ .

$\frac{- (5 x^{2}) + 25 x + 7}{(x + 7) (x - 5)}$

Factor $- 1$ out of $25 x$ .

$\frac{- (5 x^{2}) - (- 25 x) + 7}{(x + 7) (x - 5)}$

Factor $- 1$ out of $- (5 x^{2}) - (- 25 x)$ .

$\frac{- (5 x^{2} - 25 x) + 7}{(x + 7) (x - 5)}$

Rewrite $7$ as $- 1 (- 7)$ .

$\frac{- (5 x^{2} - 25 x) - 1 (- 7)}{(x + 7) (x - 5)}$

Factor $- 1$ out of $- (5 x^{2} - 25 x) - 1 (- 7)$ .

$\frac{- (5 x^{2} - 25 x - 7)}{(x + 7) (x - 5)}$

Simplify the expression.

Rewrite $- (5 x^{2} - 25 x - 7)$ as $- 1 (5 x^{2} - 25 x - 7)$ .

$\frac{- 1 (5 x^{2} - 25 x - 7)}{(x + 7) (x - 5)}$

Move the negative in front of the fraction.

$- \frac{5 x^{2} - 25 x - 7}{(x + 7) (x - 5)}$

Simplify 7/(x^2+2x-35)-(5x)/(x+7)

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