Solve x+2/x-1=x+1/x+4

$$\frac{ x+2 }{ x-1 } = \frac{ x+1 }{ x+4 }$$

Solve for x

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -4,1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(x+4\right), the least common multiple of x-1,x+4.

$$\left(x+4\right)\left(x+2\right)=\left(x-1\right)\left(x+1\right)$$

Use the distributive property to multiply x+4 by x+2 and combine like terms.

$$x^{2}+6x+8=\left(x-1\right)\left(x+1\right)$$

Consider \left(x-1\right)\left(x+1\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$x^{2}+6x+8=x^{2}-1$$

Subtract x^{2} from both sides.

$$x^{2}+6x+8-x^{2}=-1$$

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

$$6x+8=-1$$

Subtract 8 from both sides.

$$6x=-1-8$$

Subtract 8 from -1 to get -9.

$$6x=-9$$

Divide both sides by 6.

$$x=\frac{-9}{6}$$

Reduce the fraction \frac{-9}{6} to lowest terms by extracting and canceling out 3.

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