Solve 2/a^2-1/2a/frac{5{a}+2/3a}

$$\frac { \frac { 2 } { a ^ { 2 } } - \frac { 1 } { 2 a } } { \frac { 5 } { a } + \frac { 2 } { 3 a } }$$

Evaluate

$$-\frac{3}{34}+\frac{6}{17a}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a^{2} and 2a is 2a^{2}. Multiply \frac{2}{a^{2}} times \frac{2}{2}. Multiply \frac{1}{2a} times \frac{a}{a}.

$$\frac{\frac{2\times 2}{2a^{2}}-\frac{a}{2a^{2}}}{\frac{5}{a}+\frac{2}{3a}}$$

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

$$\frac{\frac{2\times 2-a}{2a^{2}}}{\frac{5}{a}+\frac{2}{3a}}$$

Do the multiplications in 2\times 2-a.

$$\frac{\frac{4-a}{2a^{2}}}{\frac{5}{a}+\frac{2}{3a}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and 3a is 3a. Multiply \frac{5}{a} times \frac{3}{3}.

$$\frac{\frac{4-a}{2a^{2}}}{\frac{5\times 3}{3a}+\frac{2}{3a}}$$

Since \frac{5\times 3}{3a} and \frac{2}{3a} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4-a}{2a^{2}}}{\frac{5\times 3+2}{3a}}$$

Do the multiplications in 5\times 3+2.

$$\frac{\frac{4-a}{2a^{2}}}{\frac{15+2}{3a}}$$

Do the calculations in 15+2.

$$\frac{\frac{4-a}{2a^{2}}}{\frac{17}{3a}}$$

Divide \frac{4-a}{2a^{2}} by \frac{17}{3a} by multiplying \frac{4-a}{2a^{2}} by the reciprocal of \frac{17}{3a}.

$$\frac{\left(4-a\right)\times 3a}{2a^{2}\times 17}$$

Cancel out a in both numerator and denominator.

$$\frac{3\left(-a+4\right)}{2\times 17a}$$

Multiply 2 and 17 to get 34.

$$\frac{3\left(-a+4\right)}{34a}$$

Use the distributive property to multiply 3 by -a+4.

$$\frac{-3a+12}{34a}$$

Expand

$$-\frac{3}{34}+\frac{6}{17a}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a^{2} and 2a is 2a^{2}. Multiply \frac{2}{a^{2}} times \frac{2}{2}. Multiply \frac{1}{2a} times \frac{a}{a}.

$$\frac{\frac{2\times 2}{2a^{2}}-\frac{a}{2a^{2}}}{\frac{5}{a}+\frac{2}{3a}}$$

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

$$\frac{\frac{2\times 2-a}{2a^{2}}}{\frac{5}{a}+\frac{2}{3a}}$$

Do the multiplications in 2\times 2-a.

$$\frac{\frac{4-a}{2a^{2}}}{\frac{5}{a}+\frac{2}{3a}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and 3a is 3a. Multiply \frac{5}{a} times \frac{3}{3}.

$$\frac{\frac{4-a}{2a^{2}}}{\frac{5\times 3}{3a}+\frac{2}{3a}}$$

Since \frac{5\times 3}{3a} and \frac{2}{3a} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4-a}{2a^{2}}}{\frac{5\times 3+2}{3a}}$$

Do the multiplications in 5\times 3+2.

$$\frac{\frac{4-a}{2a^{2}}}{\frac{15+2}{3a}}$$

Do the calculations in 15+2.

$$\frac{\frac{4-a}{2a^{2}}}{\frac{17}{3a}}$$

Divide \frac{4-a}{2a^{2}} by \frac{17}{3a} by multiplying \frac{4-a}{2a^{2}} by the reciprocal of \frac{17}{3a}.

$$\frac{\left(4-a\right)\times 3a}{2a^{2}\times 17}$$

Cancel out a in both numerator and denominator.

$$\frac{3\left(-a+4\right)}{2\times 17a}$$

Multiply 2 and 17 to get 34.

$$\frac{3\left(-a+4\right)}{34a}$$

Use the distributive property to multiply 3 by -a+4.

$$\frac{-3a+12}{34a}$$