Solve 2x+7/5x+2=2x+3/5x-1

$$\frac { 2 x + 7 } { 5 x + 2 } = \frac { 2 x + 3 } { 5 x - 1 }$$

Solve for x

$$x=\frac{13}{14}\approx 0.928571429$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{2}{5},\frac{1}{5} since division by zero is not defined. Multiply both sides of the equation by \left(5x-1\right)\left(5x+2\right), the least common multiple of 5x+2,5x-1.

$$\left(5x-1\right)\left(2x+7\right)=\left(5x+2\right)\left(2x+3\right)$$

Use the distributive property to multiply 5x-1 by 2x+7 and combine like terms.

$$10x^{2}+33x-7=\left(5x+2\right)\left(2x+3\right)$$

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

$$10x^{2}+33x-7=10x^{2}+19x+6$$

Subtract 10x^{2} from both sides.

$$10x^{2}+33x-7-10x^{2}=19x+6$$

Combine 10x^{2} and -10x^{2} to get 0.

$$33x-7=19x+6$$

Subtract 19x from both sides.

$$33x-7-19x=6$$

Combine 33x and -19x to get 14x.

$$14x-7=6$$

Add 7 to both sides.

$$14x=6+7$$

Add 6 and 7 to get 13.

$$14x=13$$

Divide both sides by 14.

$$x=\frac{13}{14}$$