what is the difference?\n$\frac{x}{x^{2}-2x - 15}-\frac{4}{x^{2}+2x - 35}$\n$\frac{x^{2}+3x + 12}{(x - 3)(x…

what is the difference?\n$\frac{x}{x^{2}-2x - 15}-\frac{4}{x^{2}+2x - 35}$\n$\frac{x^{2}+3x + 12}{(x - 3)(x - 5)(x + 7)}$\n$\frac{x(x + 3-12)}{(x + 3)(x - 5)(x + 7)}$\n$\frac{x^{2}+3x + 12}{(x + 3)(x - 5)(x + 7)}$\n$\frac{x^{2}+3x - 12}{(x + 3)(x - 5)(x + 7)}$

what is the difference?\n$\frac{x}{x^{2}-2x - 15}-\frac{4}{x^{2}+2x - 35}$\n$\frac{x^{2}+3x + 12}{(x - 3)(x - 5)(x + 7)}$\n$\frac{x(x + 3-12)}{(x + 3)(x - 5)(x + 7)}$\n$\frac{x^{2}+3x + 12}{(x + 3)(x - 5)(x + 7)}$\n$\frac{x^{2}+3x - 12}{(x + 3)(x - 5)(x + 7)}$

Answer

Answer:

$\frac{x^{2}+3x + 12}{(x + 3)(x - 5)(x+7)}$

Explanation:

Step1: Factor the denominators

$x^{2}-2x - 15=(x - 5)(x+3)$ and $x^{2}+2x - 35=(x - 5)(x + 7)$

Step2: Find the common denominator

The common denominator is $(x - 5)(x + 3)(x + 7)$

Step3: Rewrite the fractions

$\frac{x}{x^{2}-2x - 15}=\frac{x}{(x - 5)(x + 3)}=\frac{x(x + 7)}{(x - 5)(x + 3)(x + 7)}=\frac{x^{2}+7x}{(x - 5)(x + 3)(x + 7)}$ $\frac{4}{x^{2}+2x - 35}=\frac{4}{(x - 5)(x + 7)}=\frac{4(x + 3)}{(x - 5)(x + 3)(x + 7)}=\frac{4x+12}{(x - 5)(x + 3)(x + 7)}$

Step4: Subtract the fractions

$\frac{x^{2}+7x-(4x + 12)}{(x - 5)(x + 3)(x + 7)}=\frac{x^{2}+7x-4x - 12}{(x - 5)(x + 3)(x + 7)}=\frac{x^{2}+3x - 12}{(x - 5)(x + 3)(x + 7)}$