Solve 4x+7/3x-3=4x-2/3x+5

$$\frac { 4 x + 7 } { 3 x - 3 } = \frac { 4 x - 2 } { 3 x + 5 }$$

Solve for x

$$x=-\frac{29}{59}\approx -0.491525424$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{5}{3},1 since division by zero is not defined. Multiply both sides of the equation by 3\left(x-1\right)\left(3x+5\right), the least common multiple of 3x-3,3x+5.

$$\left(3x+5\right)\left(4x+7\right)=\left(3x-3\right)\left(4x-2\right)$$

Use the distributive property to multiply 3x+5 by 4x+7 and combine like terms.

$$12x^{2}+41x+35=\left(3x-3\right)\left(4x-2\right)$$

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

$$12x^{2}+41x+35=12x^{2}-18x+6$$

Subtract 12x^{2} from both sides.

$$12x^{2}+41x+35-12x^{2}=-18x+6$$

Combine 12x^{2} and -12x^{2} to get 0.

$$41x+35=-18x+6$$

Add 18x to both sides.

$$41x+35+18x=6$$

Combine 41x and 18x to get 59x.

$$59x+35=6$$

Subtract 35 from both sides.

$$59x=6-35$$

Subtract 35 from 6 to get -29.

$$59x=-29$$

Divide both sides by 59.

$$x=\frac{-29}{59}$$

Fraction \frac{-29}{59} can be rewritten as -\frac{29}{59} by extracting the negative sign.

$$x=-\frac{29}{59}$$