Question

How do you simplify `- 4/ (x - 5) + 7/ (2x + 3)`?

Answer 1

`(-x-47)/((2x+3)(x-5))` OR `(-x-47)/(2x^2-7x-15)`

Explanation:

Rearrange and write as:

`(7/(2x+3))-(4/(x-5))`

To simplify this, you need to make the denominators equal by finding their lowest common denominator (multiple). Whatever happens to the denominator, must happen to the numerator:

`7/((2x+3)(x-5))-4/((2x+3)(x-5))`

`(7(x-5))/((2x+3)(x-5))-(4(2x+3))/((2x+3)(x-5))`

Because the denominators now share the same LCM, you can merge them:

`(7(x-5)-4(2x+3))/((2x+3)(x-5))`

Multiply out all the brackets:

`(7x-35-8x-12)/(2x^2-10x+3x-15)`

Proceed to simplify terms:

`(-x-47)/(2x^2-7x-15)`

OR

Keep the denominator in the brackets:

`(-x-47)/((2x+3)(x-5))`