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

`(11x-10)/(x^2-2x)`

Given:

`(x+4)/(x-2)-(x-5)/(x)`

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

`(x(x+4)-(x-5)(x-2))/(x(x-2))`

Simplify the expression by performing the operation:

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

*Distribute the negative sign inside the parenthesis

`(x^2+4x-x^2+7x-10)/(x^2-2x)`

Simplify by adding like terms:

`\begin{gathered} (x^2+4x-x^2+7x-10)/(x^2-2x) \\ =(11x-10)/(x^2-2x) \end{gathered}`

Therefore, the final answer would be:

`(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.