Solve 9x-7/3x+5=3x-4/x+6

$$\frac { 9 x - 7 } { 3 x + 5 } = \frac { 3 x - 4 } { x + 6 }$$

Solve for x

$$x=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -6,-\frac{5}{3} since division by zero is not defined. Multiply both sides of the equation by \left(x+6\right)\left(3x+5\right), the least common multiple of 3x+5,x+6.

$$\left(x+6\right)\left(9x-7\right)=\left(3x+5\right)\left(3x-4\right)$$

Use the distributive property to multiply x+6 by 9x-7 and combine like terms.

$$9x^{2}+47x-42=\left(3x+5\right)\left(3x-4\right)$$

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

$$9x^{2}+47x-42=9x^{2}+3x-20$$

Subtract 9x^{2} from both sides.

$$9x^{2}+47x-42-9x^{2}=3x-20$$

Combine 9x^{2} and -9x^{2} to get 0.

$$47x-42=3x-20$$

Subtract 3x from both sides.

$$47x-42-3x=-20$$

Combine 47x and -3x to get 44x.

$$44x-42=-20$$

Add 42 to both sides.

$$44x=-20+42$$

Add -20 and 42 to get 22.

$$44x=22$$

Divide both sides by 44.

$$x=\frac{22}{44}$$

Reduce the fraction \frac{22}{44} to lowest terms by extracting and canceling out 22.

$$x=\frac{1}{2}$$