Question

Simplify the expression (Image below) Precalculus please help! D:

Answer 1

Answer:

$\boxed{\sf \frac{x-4}{x^2-2x} }$

Step-by-step explanation:

$\sf \cfrac{x+6}{x^2+3x}-\cfrac{5}{x^2+x-6}$

Factor x² + 3x, and x²+ x - 6

$\sf \cfrac{x+6}{x(x+3)} -\cfrac{5}{(x-2)(x+3}$

To add or subtract expressions, we expand them to make their denominators the same, LCM of x(x+3) and (x-2)(x+3) is x(x-2) (x+3).

Multiply $\sf \frac{x+6}{x(x+3)}\times \sf \frac{x-3}{x-2}$ and $\frac{5}{(x-2)(x+3)} \times \frac{x}{x}$

$\sf \cfrac{(x+6)(x-2)}{x(x-2)(x+3)}-\cfrac{5x}{x(x-2)(x+3)}$

Here, $\sf \frac{(x+6)(x-2)}{x(x-2)(x+3)}$  and $\sf \frac{5x}{x(x-2)(x+3}$ have the same denominators, we will subtract them by subtracting their numerators:

$\sf \cfrac{(x+6)(x-2)-5x}{x(x-2)(x+3)}$

*Multiply (x+6)(x-2)-5x:

$\sf \cfrac{x^2-2x+6x-12-5x}{x(x-2)(x+3)}$

Combine like terms: x² - 2x + 6x - 12 - 5x

$\sf \cfrac{-x-12+x^2}{x(x-2)(x+3)}$

Now, factor expressions that are not already factored:

$\sf \cfrac{(x-4)(x+3)}{x(x-2)(x+3)}$

$\sf \cfrac{x-4}{x(x-2)}$

Expand:

$\sf \cfrac{x-4}{x^2-2x}$

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