Solve 1/frac{1{4}(2-x)(2+x)}

$$\frac { 1 } { \frac { 1 } { 4 } ( 2 - x ) ( 2 + x ) }$$

Evaluate

$$\frac{4}{4-x^{2}}$$

Solution Steps

Use the distributive property to multiply \frac{1}{4} by 2-x.

$$\frac{1}{\left(\frac{1}{4}\times 2+\frac{1}{4}\left(-1\right)x\right)\left(2+x\right)}$$

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

$$\frac{1}{\left(\frac{2}{4}+\frac{1}{4}\left(-1\right)x\right)\left(2+x\right)}$$

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

$$\frac{1}{\left(\frac{1}{2}+\frac{1}{4}\left(-1\right)x\right)\left(2+x\right)}$$

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

$$\frac{1}{\left(\frac{1}{2}-\frac{1}{4}x\right)\left(2+x\right)}$$

Apply the distributive property by multiplying each term of \frac{1}{2}-\frac{1}{4}x by each term of 2+x.

$$\frac{1}{\frac{1}{2}\times 2+\frac{1}{2}x-\frac{1}{4}x\times 2-\frac{1}{4}xx}$$

Multiply x and x to get x^{2}.

$$\frac{1}{\frac{1}{2}\times 2+\frac{1}{2}x-\frac{1}{4}x\times 2-\frac{1}{4}x^{2}}$$

Cancel out 2 and 2.

$$\frac{1}{1+\frac{1}{2}x-\frac{1}{4}x\times 2-\frac{1}{4}x^{2}}$$

Express -\frac{1}{4}\times 2 as a single fraction.

$$\frac{1}{1+\frac{1}{2}x+\frac{-2}{4}x-\frac{1}{4}x^{2}}$$

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

$$\frac{1}{1+\frac{1}{2}x-\frac{1}{2}x-\frac{1}{4}x^{2}}$$

Combine \frac{1}{2}x and -\frac{1}{2}x to get 0.

$$\frac{1}{1-\frac{1}{4}x^{2}}$$

Expand

$$\frac{4}{4-x^{2}}$$

Solution Steps

Use the distributive property to multiply \frac{1}{4} by 2-x.

$$\frac{1}{\left(\frac{1}{4}\times 2+\frac{1}{4}\left(-1\right)x\right)\left(2+x\right)}$$

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

$$\frac{1}{\left(\frac{2}{4}+\frac{1}{4}\left(-1\right)x\right)\left(2+x\right)}$$

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

$$\frac{1}{\left(\frac{1}{2}+\frac{1}{4}\left(-1\right)x\right)\left(2+x\right)}$$

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

$$\frac{1}{\left(\frac{1}{2}-\frac{1}{4}x\right)\left(2+x\right)}$$

Apply the distributive property by multiplying each term of \frac{1}{2}-\frac{1}{4}x by each term of 2+x.

$$\frac{1}{\frac{1}{2}\times 2+\frac{1}{2}x-\frac{1}{4}x\times 2-\frac{1}{4}xx}$$

Multiply x and x to get x^{2}.

$$\frac{1}{\frac{1}{2}\times 2+\frac{1}{2}x-\frac{1}{4}x\times 2-\frac{1}{4}x^{2}}$$

Cancel out 2 and 2.

$$\frac{1}{1+\frac{1}{2}x-\frac{1}{4}x\times 2-\frac{1}{4}x^{2}}$$

Express -\frac{1}{4}\times 2 as a single fraction.

$$\frac{1}{1+\frac{1}{2}x+\frac{-2}{4}x-\frac{1}{4}x^{2}}$$

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

$$\frac{1}{1+\frac{1}{2}x-\frac{1}{2}x-\frac{1}{4}x^{2}}$$

Combine \frac{1}{2}x and -\frac{1}{2}x to get 0.

$$\frac{1}{1-\frac{1}{4}x^{2}}$$