Solve 25+1/a^2-10/a/5-frac{1{a}}*a

$$\frac { 25 + \frac { 1 } { a ^ { 2 } } - \frac { 10 } { a } } { 5 - \frac { 1 } { a } } \cdot a$$

Evaluate

$$5a-1$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 25 times \frac{a^{2}}{a^{2}}.

$$\frac{\frac{25a^{2}}{a^{2}}+\frac{1}{a^{2}}-\frac{10}{a}}{5-\frac{1}{a}}a$$

Since \frac{25a^{2}}{a^{2}} and \frac{1}{a^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{25a^{2}+1}{a^{2}}-\frac{10}{a}}{5-\frac{1}{a}}a$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a^{2} and a is a^{2}. Multiply \frac{10}{a} times \frac{a}{a}.

$$\frac{\frac{25a^{2}+1}{a^{2}}-\frac{10a}{a^{2}}}{5-\frac{1}{a}}a$$

Since \frac{25a^{2}+1}{a^{2}} and \frac{10a}{a^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{25a^{2}+1-10a}{a^{2}}}{5-\frac{1}{a}}a$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{a}{a}.

$$\frac{\frac{25a^{2}+1-10a}{a^{2}}}{\frac{5a}{a}-\frac{1}{a}}a$$

Since \frac{5a}{a} and \frac{1}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{25a^{2}+1-10a}{a^{2}}}{\frac{5a-1}{a}}a$$

Divide \frac{25a^{2}+1-10a}{a^{2}} by \frac{5a-1}{a} by multiplying \frac{25a^{2}+1-10a}{a^{2}} by the reciprocal of \frac{5a-1}{a}.

$$\frac{\left(25a^{2}+1-10a\right)a}{a^{2}\left(5a-1\right)}a$$

Cancel out a in both numerator and denominator.

$$\frac{25a^{2}-10a+1}{a\left(5a-1\right)}a$$

Factor the expressions that are not already factored in \frac{25a^{2}-10a+1}{a\left(5a-1\right)}.

$$\frac{\left(5a-1\right)^{2}}{a\left(5a-1\right)}a$$

Cancel out 5a-1 in both numerator and denominator.

$$\frac{5a-1}{a}a$$

Cancel out a and a.

$$5a-1$$

Expand

$$5a-1$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 25 times \frac{a^{2}}{a^{2}}.

$$\frac{\frac{25a^{2}}{a^{2}}+\frac{1}{a^{2}}-\frac{10}{a}}{5-\frac{1}{a}}a$$

Since \frac{25a^{2}}{a^{2}} and \frac{1}{a^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{25a^{2}+1}{a^{2}}-\frac{10}{a}}{5-\frac{1}{a}}a$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a^{2} and a is a^{2}. Multiply \frac{10}{a} times \frac{a}{a}.

$$\frac{\frac{25a^{2}+1}{a^{2}}-\frac{10a}{a^{2}}}{5-\frac{1}{a}}a$$

Since \frac{25a^{2}+1}{a^{2}} and \frac{10a}{a^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{25a^{2}+1-10a}{a^{2}}}{5-\frac{1}{a}}a$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{a}{a}.

$$\frac{\frac{25a^{2}+1-10a}{a^{2}}}{\frac{5a}{a}-\frac{1}{a}}a$$

Since \frac{5a}{a} and \frac{1}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{25a^{2}+1-10a}{a^{2}}}{\frac{5a-1}{a}}a$$

Divide \frac{25a^{2}+1-10a}{a^{2}} by \frac{5a-1}{a} by multiplying \frac{25a^{2}+1-10a}{a^{2}} by the reciprocal of \frac{5a-1}{a}.

$$\frac{\left(25a^{2}+1-10a\right)a}{a^{2}\left(5a-1\right)}a$$

Cancel out a in both numerator and denominator.

$$\frac{25a^{2}-10a+1}{a\left(5a-1\right)}a$$

Factor the expressions that are not already factored in \frac{25a^{2}-10a+1}{a\left(5a-1\right)}.

$$\frac{\left(5a-1\right)^{2}}{a\left(5a-1\right)}a$$

Cancel out 5a-1 in both numerator and denominator.

$$\frac{5a-1}{a}a$$

Cancel out a and a.

$$5a-1$$