Solve x+4/x+1-1/3x-2=x-3/x+1

$$\frac { x + 4 } { x + 1 } - \frac { 1 } { 3 x - 2 } = \frac { x - 3 } { x + 1 }$$

Solve for x

$$x=\frac{3}{4}=0.75$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -1,\frac{2}{3} since division by zero is not defined. Multiply both sides of the equation by \left(3x-2\right)\left(x+1\right), the least common multiple of x+1,3x-2.

$$\left(3x-2\right)\left(x+4\right)-\left(x+1\right)=\left(3x-2\right)\left(x-3\right)$$

Use the distributive property to multiply 3x-2 by x+4 and combine like terms.

$$3x^{2}+10x-8-\left(x+1\right)=\left(3x-2\right)\left(x-3\right)$$

To find the opposite of x+1, find the opposite of each term.

$$3x^{2}+10x-8-x-1=\left(3x-2\right)\left(x-3\right)$$

Combine 10x and -x to get 9x.

$$3x^{2}+9x-8-1=\left(3x-2\right)\left(x-3\right)$$

Subtract 1 from -8 to get -9.

$$3x^{2}+9x-9=\left(3x-2\right)\left(x-3\right)$$

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

$$3x^{2}+9x-9=3x^{2}-11x+6$$

Subtract 3x^{2} from both sides.

$$3x^{2}+9x-9-3x^{2}=-11x+6$$

Combine 3x^{2} and -3x^{2} to get 0.

$$9x-9=-11x+6$$

Add 11x to both sides.

$$9x-9+11x=6$$

Combine 9x and 11x to get 20x.

$$20x-9=6$$

Add 9 to both sides.

$$20x=6+9$$

Add 6 and 9 to get 15.

$$20x=15$$

Divide both sides by 20.

$$x=\frac{15}{20}$$

Reduce the fraction \frac{15}{20} to lowest terms by extracting and canceling out 5.

$$x=\frac{3}{4}$$