Question

What is the simplified form of `3/(2x+5) + 21/(8x^2 + 26x + 15)`?

Answer 1

`3/(2x+5)+21/(8x^2+26x+15)=(12x^2+9x+21)/(8x^2+26x+15)`

Explanation:

For this we should factorize `8x^2+26x+15`. Splitting the middle term we get `8x^2+20x+6x+15`

= `4x(2x+5)+3(2x+5)=(4x+3)(2x+5)`

Hence, `3/(2x+5)+21/(8x^2+26x+15)`

= `3/(2x+5)+21/((4x+3)(2x+5))`

= `(3x(4x+3)+21)/((4x+3)(2x+5))`

= `(12x^2+9x+21)/(8x^2+26x+15)`