Solve 2x+5/4x+1=3x+5/6x-1

$$\frac { 2 x + 5 } { 4 x + 1 } = \frac { 3 x + 5 } { 6 x - 1 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

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

$$\left(6x-1\right)\left(2x+5\right)=\left(4x+1\right)\left(3x+5\right)$$

Use the distributive property to multiply 6x-1 by 2x+5 and combine like terms.

$$12x^{2}+28x-5=\left(4x+1\right)\left(3x+5\right)$$

Use the distributive property to multiply 4x+1 by 3x+5 and combine like terms.

$$12x^{2}+28x-5=12x^{2}+23x+5$$

Subtract 12x^{2} from both sides.

$$12x^{2}+28x-5-12x^{2}=23x+5$$

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

$$28x-5=23x+5$$

Subtract 23x from both sides.

$$28x-5-23x=5$$

Combine 28x and -23x to get 5x.

$$5x-5=5$$

Add 5 to both sides.

$$5x=5+5$$

Add 5 and 5 to get 10.

$$5x=10$$

Divide both sides by 5.

$$x=\frac{10}{5}$$

Divide 10 by 5 to get 2.

$$x=2$$