Question

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

Answer 1

Answer: x =
`-(5)/(2)`, 2

Explanation:

We will solve for x in the given equation.

Given:

`\displaystyle (5)/((x + 3))+(4)/((x + 2)) = 2`

Get common denominators:

`\displaystyle (5(x + 2))/((x + 3)(x + 2))+(4(x + 3))/((x + 3)(x + 2)) = 2`

Addition:

`\displaystyle (5(x + 2)+4(x + 3))/((x + 3)(x + 2)) = 2`

Multiply both sides of the equation by (x+3)(x+2):

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

Distribute and multiply:

5x + 10 + 4x + 12 = 2x² + 10x + 12

Get all terms on one side of the equation by subtracting from both sides:

-2x² + 5x - 10 x+ 10 + 4x + 12 - 12 = 0

Simplify by combing like terms:

-2x² - x + 10 = 0

Factor:

-1(x - 2)(2x + 5) = 0

Solve for x:

x =
`-(5)/(2)`, 2