Solve 1/a-3/2-a=4/a^2-2a

$$\frac { 1 } { a } - \frac { 3 } { 2 - a } = \frac { 4 } { a ^ { 2 } - 2 a }$$

Solve for a

$$a = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

Variable a cannot be equal to any of the values 0,2 since division by zero is not defined. Multiply both sides of the equation by a\left(a-2\right), the least common multiple of a,2-a,a^{2}-2a.

$$a-2-\left(-a\times 3\right)=4$$

Multiply -1 and 3 to get -3.

$$a-2-\left(-3a\right)=4$$

The opposite of -3a is 3a.

$$a-2+3a=4$$

Combine a and 3a to get 4a.

$$4a-2=4$$

Add 2 to both sides.

$$4a=4+2$$

Add 4 and 2 to get 6.

$$4a=6$$

Divide both sides by 4.

$$a=\frac{6}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$a=\frac{3}{2}$$