Solve 2x-5/2x-6+5/x-3=1/4x-12

$$\frac { 2 x - 5 } { 2 x - 6 } + \frac { 5 } { x - 3 } = \frac { 1 } { 4 x - 12 }$$

Solve for x

$$x = -\frac{9}{4} = -2\frac{1}{4} = -2.25$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by 4\left(x-3\right), the least common multiple of 2x-6,x-3,4x-12.

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

Use the distributive property to multiply 2 by 2x-5.

$$4x-10+4\times 5=1$$

Multiply 4 and 5 to get 20.

$$4x-10+20=1$$

Add -10 and 20 to get 10.

$$4x+10=1$$

Subtract 10 from both sides.

$$4x=1-10$$

Subtract 10 from 1 to get -9.

$$4x=-9$$

Divide both sides by 4.

$$x=\frac{-9}{4}$$

Fraction \frac{-9}{4} can be rewritten as -\frac{9}{4} by extracting the negative sign.

$$x=-\frac{9}{4}$$