Question

1/(x+1)+1/(x+2)=2/(x-3)

Answer 1

1/(x+1)+1/(x+2)=2/(x-3)=-1 4/9

Answer 2

To solve the equation:

1/(x+1) + 1/(x+2) = 2/(x-3)

We'll start by finding a common denominator for the fractions on the left side of the equation.

The common denominator will be (x+1)(x+2)(x-3). Multiplying both sides of the equation by this common denominator will help us eliminate the denominators.

Let's go through the steps:

Multiply both sides of the equation by (x+1)(x+2)(x-3):

[(x+1)(x+2)(x-3)] * [1/(x+1) + 1/(x+2)] = [(x+1)(x+2)(x-3)] * [2/(x-3)]

Cancel out the denominators:

(x+2)(x-3) + (x+1)(x-3) = 2(x+1)(x+2)

Expand the terms:

(x^2 - x - 6) + (x^2 - 2x - 3) = 2(x^2 + 3x + 2)

Combine like terms:

2x^2 - 3x - 9 = 2x^2 + 6x + 4

Simplify by canceling out the common terms (2x^2):

-3x - 9 = 6x + 4

Move all the variables to one side and constants to the other:

-9 - 4 = 6x + 3x

-13 = 9x

Divide both sides by 9:

x = -13/9

Therefore, the solution to the equation is x = -13/9.