Solve 4/varepsilondiv(9/2+9/3)=?

$$\frac { 4 } { \varepsilon } \div ( \frac { 9 } { 2 } + \frac { 9 } { 3 } ) = ?$$

Evaluate

$$\frac{8}{15\epsilon }$$

Solution Steps

Divide 9 by 3 to get 3.

$$\frac{\frac{4}{\epsilon }}{\frac{9}{2}+3}$$

Convert 3 to fraction \frac{6}{2}.

$$\frac{\frac{4}{\epsilon }}{\frac{9}{2}+\frac{6}{2}}$$

Since \frac{9}{2} and \frac{6}{2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4}{\epsilon }}{\frac{9+6}{2}}$$

Add 9 and 6 to get 15.

$$\frac{\frac{4}{\epsilon }}{\frac{15}{2}}$$

Divide \frac{4}{\epsilon } by \frac{15}{2} by multiplying \frac{4}{\epsilon } by the reciprocal of \frac{15}{2}.

$$\frac{4\times 2}{\epsilon \times 15}$$

Multiply 4 and 2 to get 8.

$$\frac{8}{\epsilon \times 15}$$

Differentiate w.r.t. ε

$$-\frac{8}{15\epsilon ^{2}}$$