Question

I don’t understand why the -5+-2 is 7…x? Why do we put the x?? Also why is -5*-2=-10? Shouldn’t it be 10?

Answer 1

Answer:

$\frac{11x-10}{x^2-2x}$

Given:

$\frac{x+4}{x-2}-\frac{x-5}{x}$

First, we will find the common denominator for us to be able to subtract the terms:

$\frac{x(x+4)-(x-5)(x-2)}{x(x-2)}$

Simplify the expression by performing the operation:

$\begin{gathered} \frac{x^2+4x-(x^2-5x-2x+10)}{x^2-2x} \\ =\frac{x^2+4x-(x^2-7x+10)}{x^2-2x} \end{gathered}$

*Distribute the negative sign inside the parenthesis

$\frac{x^2+4x-x^2+7x-10}{x^2-2x}$

Simplify by adding like terms:

$\begin{gathered} \frac{x^2+4x-x^2+7x-10}{x^2-2x} \\ =\frac{11x-10}{x^2-2x} \end{gathered}$

Therefore, the final answer would be:

$\frac{11x-10}{x^2-2x}$

Note:

The -7x and 10 became the opposite signs because we had to distribute the negative sign present before the parenthesis that indicates the subtraction operation.