Solve 4(a-1)x1/2-(a-1)^2/4(a-1)=1/4

$$\frac { 4 ( a - 1 ) x \frac { 1 } { 2 } - ( a - 1 ) ^ { 2 } } { 4 ( a - 1 ) } = \frac { 1 } { 4 }$$

Solve for x

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

$$a\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4\left(a-1\right), the least common multiple of 4\left(a-1\right),4.

$$4\left(a-1\right)x\times \frac{1}{2}-\left(a-1\right)^{2}=a-1$$

Multiply 4 and \frac{1}{2} to get 2.

$$2\left(a-1\right)x-\left(a-1\right)^{2}=a-1$$

Use the distributive property to multiply 2 by a-1.

$$\left(2a-2\right)x-\left(a-1\right)^{2}=a-1$$

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

$$2ax-2x-\left(a-1\right)^{2}=a-1$$

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(a-1\right)^{2}.

$$2ax-2x-\left(a^{2}-2a+1\right)=a-1$$

To find the opposite of a^{2}-2a+1, find the opposite of each term.

$$2ax-2x-a^{2}+2a-1=a-1$$

Add a^{2} to both sides.

$$2ax-2x+2a-1=a-1+a^{2}$$

Subtract 2a from both sides.

$$2ax-2x-1=a-1+a^{2}-2a$$

Combine a and -2a to get -a.

$$2ax-2x-1=-a-1+a^{2}$$

Add 1 to both sides.

$$2ax-2x=-a-1+a^{2}+1$$

Add -1 and 1 to get 0.

$$2ax-2x=-a+a^{2}$$

Combine all terms containing x.

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

The equation is in standard form.

$$\left(2a-2\right)x=a^{2}-a$$

Divide both sides by 2a-2.

$$\frac{\left(2a-2\right)x}{2a-2}=\frac{a\left(a-1\right)}{2a-2}$$

Dividing by 2a-2 undoes the multiplication by 2a-2.

$$x=\frac{a\left(a-1\right)}{2a-2}$$

Divide a\left(-1+a\right) by 2a-2.

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

Solve for a

$$a=2x$$

$$x\neq \frac{1}{2}$$