Solve 1/4-1/a/frac{4-a{4}}

$$\frac { \frac { 1 } { 4 } - \frac { 1 } { a } } { \frac { 4 - a } { 4 } }$$

Evaluate

$$-\frac{1}{a}$$

Solution Steps

Divide \frac{1}{4}-\frac{1}{a} by \frac{4-a}{4} by multiplying \frac{1}{4}-\frac{1}{a} by the reciprocal of \frac{4-a}{4}.

$$\frac{\left(\frac{1}{4}-\frac{1}{a}\right)\times 4}{4-a}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and a is 4a. Multiply \frac{1}{4} times \frac{a}{a}. Multiply \frac{1}{a} times \frac{4}{4}.

$$\frac{\left(\frac{a}{4a}-\frac{4}{4a}\right)\times 4}{4-a}$$

Since \frac{a}{4a} and \frac{4}{4a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{a-4}{4a}\times 4}{4-a}$$

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

$$\frac{\frac{\left(a-4\right)\times 4}{4a}}{4-a}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\frac{a-4}{a}}{4-a}$$

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

$$\frac{a-4}{a\left(4-a\right)}$$

Extract the negative sign in a-4.

$$\frac{-\left(-a+4\right)}{a\left(-a+4\right)}$$

Cancel out -a+4 in both numerator and denominator.

$$\frac{-1}{a}$$

Expand

$$-\frac{1}{a}$$

Solution Steps

Divide \frac{1}{4}-\frac{1}{a} by \frac{4-a}{4} by multiplying \frac{1}{4}-\frac{1}{a} by the reciprocal of \frac{4-a}{4}.

$$\frac{\left(\frac{1}{4}-\frac{1}{a}\right)\times 4}{4-a}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and a is 4a. Multiply \frac{1}{4} times \frac{a}{a}. Multiply \frac{1}{a} times \frac{4}{4}.

$$\frac{\left(\frac{a}{4a}-\frac{4}{4a}\right)\times 4}{4-a}$$

Since \frac{a}{4a} and \frac{4}{4a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{a-4}{4a}\times 4}{4-a}$$

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

$$\frac{\frac{\left(a-4\right)\times 4}{4a}}{4-a}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\frac{a-4}{a}}{4-a}$$

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

$$\frac{a-4}{a\left(4-a\right)}$$

Extract the negative sign in a-4.

$$\frac{-\left(-a+4\right)}{a\left(-a+4\right)}$$

Cancel out -a+4 in both numerator and denominator.

$$\frac{-1}{a}$$