Solve x-2/x+5+2/3x+2=x+7/x+5

$$\frac { x - 2 } { x + 5 } + \frac { 2 } { 3 x + 2 } = \frac { x + 7 } { x + 5 }$$

Solve for x

$$x=-\frac{8}{25}=-0.32$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -5,-\frac{2}{3} since division by zero is not defined. Multiply both sides of the equation by \left(x+5\right)\left(3x+2\right), the least common multiple of x+5,3x+2.

$$\left(3x+2\right)\left(x-2\right)+\left(x+5\right)\times 2=\left(3x+2\right)\left(x+7\right)$$

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

$$3x^{2}-4x-4+\left(x+5\right)\times 2=\left(3x+2\right)\left(x+7\right)$$

Use the distributive property to multiply x+5 by 2.

$$3x^{2}-4x-4+2x+10=\left(3x+2\right)\left(x+7\right)$$

Combine -4x and 2x to get -2x.

$$3x^{2}-2x-4+10=\left(3x+2\right)\left(x+7\right)$$

Add -4 and 10 to get 6.

$$3x^{2}-2x+6=\left(3x+2\right)\left(x+7\right)$$

Use the distributive property to multiply 3x+2 by x+7 and combine like terms.

$$3x^{2}-2x+6=3x^{2}+23x+14$$

Subtract 3x^{2} from both sides.

$$3x^{2}-2x+6-3x^{2}=23x+14$$

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

$$-2x+6=23x+14$$

Subtract 23x from both sides.

$$-2x+6-23x=14$$

Combine -2x and -23x to get -25x.

$$-25x+6=14$$

Subtract 6 from both sides.

$$-25x=14-6$$

Subtract 6 from 14 to get 8.

$$-25x=8$$

Divide both sides by -25.

$$x=\frac{8}{-25}$$

Fraction \frac{8}{-25} can be rewritten as -\frac{8}{25} by extracting the negative sign.

$$x=-\frac{8}{25}$$