Solve 2+2x-3/2x+3=3x+5/x+4

$$2 + \frac { 2 x - 3 } { 2 x + 3 } = \frac { 3 x + 5 } { x + 4 }$$

Solve for x

$$x=\frac{3}{8}=0.375$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -4,-\frac{3}{2} since division by zero is not defined. Multiply both sides of the equation by \left(x+4\right)\left(2x+3\right), the least common multiple of 2x+3,x+4.

$$\left(x+4\right)\left(2x+3\right)\times 2+\left(x+4\right)\left(2x-3\right)=\left(2x+3\right)\left(3x+5\right)$$

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

$$\left(2x^{2}+11x+12\right)\times 2+\left(x+4\right)\left(2x-3\right)=\left(2x+3\right)\left(3x+5\right)$$

Use the distributive property to multiply 2x^{2}+11x+12 by 2.

$$4x^{2}+22x+24+\left(x+4\right)\left(2x-3\right)=\left(2x+3\right)\left(3x+5\right)$$

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

$$4x^{2}+22x+24+2x^{2}+5x-12=\left(2x+3\right)\left(3x+5\right)$$

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

$$6x^{2}+22x+24+5x-12=\left(2x+3\right)\left(3x+5\right)$$

Combine 22x and 5x to get 27x.

$$6x^{2}+27x+24-12=\left(2x+3\right)\left(3x+5\right)$$

Subtract 12 from 24 to get 12.

$$6x^{2}+27x+12=\left(2x+3\right)\left(3x+5\right)$$

Use the distributive property to multiply 2x+3 by 3x+5 and combine like terms.

$$6x^{2}+27x+12=6x^{2}+19x+15$$

Subtract 6x^{2} from both sides.

$$6x^{2}+27x+12-6x^{2}=19x+15$$

Combine 6x^{2} and -6x^{2} to get 0.

$$27x+12=19x+15$$

Subtract 19x from both sides.

$$27x+12-19x=15$$

Combine 27x and -19x to get 8x.

$$8x+12=15$$

Subtract 12 from both sides.

$$8x=15-12$$

Subtract 12 from 15 to get 3.

$$8x=3$$

Divide both sides by 8.

$$x=\frac{3}{8}$$