Question

How do you add `\frac { x - 4} { 2x ^ { 2} + 9x - 5} + \frac { x + 3} { x ^ { 2} + 5x }`?

Answer 1

`(3x^2 + x - 3)/((x)(x + 5)(2x- 1))`

Explanation:

Factor the denominators to discover the least common denominator (LCD).

`2x^2 + 9x - 5 = 2x^2 + 10x - x - 5 = 2x(x + 5) - (x + 5) = (2x- 1)(x + 5)`

`x^2 + 5x= x(x + 5)`

Therefore, the LCD is `color(green)((x)(x + 5)(2x - 1))`.

`=>(x(x- 4))/((x)(x+ 5)(2x- 1)) + ((x+ 3)(2x- 1))/((x)(x + 5)(2x- 1))`

`=>(x^2 -4x + 2x^2 + 6x- x - 3)/((x)(x+ 5)(2x - 1))`

`=>(3x^2 + x - 3)/((x)(x + 5)(2x- 1))`

Hopefully this helps!