Solve left(2x+3right)left(x-4right)/left(2x-4right)left(x+5right)=1

$$\frac{ \left( 2x+3 \right) \left( x-4 \right) }{ \left( 2x-4 \right) \left( x+5 \right) } = 1$$

Solve for x

$$x=\frac{8}{11}\approx 0.727272727$$

Steps for Solving Linear Equation

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

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

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

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

Use the distributive property to multiply 2 by x-2.

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

Use the distributive property to multiply 2x-4 by x+5 and combine like terms.

$$2x^{2}-5x-12=2x^{2}+6x-20$$

Subtract 2x^{2} from both sides.

$$2x^{2}-5x-12-2x^{2}=6x-20$$

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

$$-5x-12=6x-20$$

Subtract 6x from both sides.

$$-5x-12-6x=-20$$

Combine -5x and -6x to get -11x.

$$-11x-12=-20$$

Add 12 to both sides.

$$-11x=-20+12$$

Add -20 and 12 to get -8.

$$-11x=-8$$

Divide both sides by -11.

$$x=\frac{-8}{-11}$$

Fraction \frac{-8}{-11} can be simplified to \frac{8}{11} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{8}{11}$$