Solve x+2(-2x+1)/3x+5=3x^2/3x+5

$$x + \frac { 2 ( - 2 x + 1 ) } { 3 x + 5 } = \frac { 3 x ^ { 2 } } { 3 x + 5 }$$

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{5}{3} since division by zero is not defined. Multiply both sides of the equation by 3x+5.

$$\left(3x+5\right)x+2\left(-2x+1\right)=3x^{2}$$

Use the distributive property to multiply 3x+5 by x.

$$3x^{2}+5x+2\left(-2x+1\right)=3x^{2}$$

Use the distributive property to multiply 2 by -2x+1.

$$3x^{2}+5x-4x+2=3x^{2}$$

Combine 5x and -4x to get x.

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

Subtract 3x^{2} from both sides.

$$3x^{2}+x+2-3x^{2}=0$$

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

$$x+2=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$x=-2$$