Solve x+1/x+2=x-3/x+1

$$\frac { x + 1 } { x + 2 } = \frac { x - 3 } { x + 1 }$$

Solve for x

$$x = -\frac{7}{3} = -2\frac{1}{3} \approx -2.333333333$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -2,-1 since division by zero is not defined. Multiply both sides of the equation by \left(x+1\right)\left(x+2\right), the least common multiple of x+2,x+1.

$$\left(x+1\right)\left(x+1\right)=\left(x+2\right)\left(x-3\right)$$

Multiply x+1 and x+1 to get \left(x+1\right)^{2}.

$$\left(x+1\right)^{2}=\left(x+2\right)\left(x-3\right)$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$x^{2}+2x+1=\left(x+2\right)\left(x-3\right)$$

Use the distributive property to multiply x+2 by x-3 and combine like terms.

$$x^{2}+2x+1=x^{2}-x-6$$

Subtract x^{2} from both sides.

$$x^{2}+2x+1-x^{2}=-x-6$$

Combine x^{2} and -x^{2} to get 0.

$$2x+1=-x-6$$

Add x to both sides.

$$2x+1+x=-6$$

Combine 2x and x to get 3x.

$$3x+1=-6$$

Subtract 1 from both sides.

$$3x=-6-1$$

Subtract 1 from -6 to get -7.

$$3x=-7$$

Divide both sides by 3.

$$x=\frac{-7}{3}$$

Fraction \frac{-7}{3} can be rewritten as -\frac{7}{3} by extracting the negative sign.

$$x=-\frac{7}{3}$$