Solve 6x^2+13x-4/2x+5=12x^2+5x-2/4x+3

$$\frac { 6 x ^ { 2 } + 13 x - 4 } { 2 x + 5 } = \frac { 12 x ^ { 2 } + 5 x - 2 } { 4 x + 3 }$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{5}{2},-\frac{3}{4} since division by zero is not defined. Multiply both sides of the equation by \left(2x+5\right)\left(4x+3\right), the least common multiple of 2x+5,4x+3.

$$\left(4x+3\right)\left(6x^{2}+13x-4\right)=\left(2x+5\right)\left(12x^{2}+5x-2\right)$$

Use the distributive property to multiply 4x+3 by 6x^{2}+13x-4 and combine like terms.

$$24x^{3}+70x^{2}+23x-12=\left(2x+5\right)\left(12x^{2}+5x-2\right)$$

Use the distributive property to multiply 2x+5 by 12x^{2}+5x-2 and combine like terms.

$$24x^{3}+70x^{2}+23x-12=24x^{3}+70x^{2}+21x-10$$

Subtract 24x^{3} from both sides.

$$24x^{3}+70x^{2}+23x-12-24x^{3}=70x^{2}+21x-10$$

Combine 24x^{3} and -24x^{3} to get 0.

$$70x^{2}+23x-12=70x^{2}+21x-10$$

Subtract 70x^{2} from both sides.

$$70x^{2}+23x-12-70x^{2}=21x-10$$

Combine 70x^{2} and -70x^{2} to get 0.

$$23x-12=21x-10$$

Subtract 21x from both sides.

$$23x-12-21x=-10$$

Combine 23x and -21x to get 2x.

$$2x-12=-10$$

Add 12 to both sides.

$$2x=-10+12$$

Add -10 and 12 to get 2.

$$2x=2$$

Divide both sides by 2.

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

Divide 2 by 2 to get 1.

$$x=1$$