Solve x+1/x+3-x/x-2=3x+2/x^2+x-6

$$\frac { x + 1 } { x + 3 } - \frac { x } { x - 2 } = \frac { 3 x + 2 } { x ^ { 2 } + x - 6 }$$

Solve for x

$$x=-\frac{4}{7}\approx -0.571428571$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3,2 since division by zero is not defined. Multiply both sides of the equation by \left(x-2\right)\left(x+3\right), the least common multiple of x+3,x-2,x^{2}+x-6.

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

Use the distributive property to multiply x-2 by x+1 and combine like terms.

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

Use the distributive property to multiply x+3 by x.

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

To find the opposite of x^{2}+3x, find the opposite of each term.

$$x^{2}-x-2-x^{2}-3x=3x+2$$

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

$$-x-2-3x=3x+2$$

Combine -x and -3x to get -4x.

$$-4x-2=3x+2$$

Subtract 3x from both sides.

$$-4x-2-3x=2$$

Combine -4x and -3x to get -7x.

$$-7x-2=2$$

Add 2 to both sides.

$$-7x=2+2$$

Add 2 and 2 to get 4.

$$-7x=4$$

Divide both sides by -7.

$$x=\frac{4}{-7}$$

Fraction \frac{4}{-7} can be rewritten as -\frac{4}{7} by extracting the negative sign.

$$x=-\frac{4}{7}$$