Solve 9x-7/(6x+5)=6x-3/4x+2

$$\frac { 9 x - 7 } { ( 6 x + 5 ) } = \frac { 6 x - 3 } { 4 x + 2 }$$

Solve for x

$$x=\frac{1}{22}\approx 0.045454545$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{5}{6},-\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 2\left(2x+1\right)\left(6x+5\right), the least common multiple of 6x+5,4x+2.

$$\left(4x+2\right)\left(9x-7\right)=\left(6x+5\right)\left(6x-3\right)$$

Use the distributive property to multiply 4x+2 by 9x-7 and combine like terms.

$$36x^{2}-10x-14=\left(6x+5\right)\left(6x-3\right)$$

Use the distributive property to multiply 6x+5 by 6x-3 and combine like terms.

$$36x^{2}-10x-14=36x^{2}+12x-15$$

Subtract 36x^{2} from both sides.

$$36x^{2}-10x-14-36x^{2}=12x-15$$

Combine 36x^{2} and -36x^{2} to get 0.

$$-10x-14=12x-15$$

Subtract 12x from both sides.

$$-10x-14-12x=-15$$

Combine -10x and -12x to get -22x.

$$-22x-14=-15$$

Add 14 to both sides.

$$-22x=-15+14$$

Add -15 and 14 to get -1.

$$-22x=-1$$

Divide both sides by -22.

$$x=\frac{-1}{-22}$$

Fraction \frac{-1}{-22} can be simplified to \frac{1}{22} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{1}{22}$$