Question

Solving Rational Functions Zoom in for a closer look Please help I've been stuck for awhile ​

Answer 1

x = 4

Explanation:

Given

`(3)/(x+4)` -
`(1)/(x+3)` =
`(x+9)/(x^2+7x+12)` ← factor the quadratic

`(3)/(x+4)` -
`(1)/(x+3)` =
`(x+9)/((x+3)(x+4))`

Multiply through by (x + 3)(x + 4) to clear the fractions

3(x+3) - (x + 4) = x + 9 ← distribute and simplify left side

3x + 9 - x - 4 = x + 9

2x + 5 = x + 9 ( subtract x from both sides )

x + 5 = 9 ( subtract 5 from both sides )

x = 4