Solve 4/frac{4{3x}+2/2y}

$$\frac { 4 } { \frac { 4 } { 3 x } + \frac { 2 } { 2 y } }$$

Evaluate

$$\frac{12xy}{3x+4y}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x and 2y is 6xy. Multiply \frac{4}{3x} times \frac{2y}{2y}. Multiply \frac{2}{2y} times \frac{3x}{3x}.

$$\frac{4}{\frac{4\times 2y}{6xy}+\frac{2\times 3x}{6xy}}$$

Since \frac{4\times 2y}{6xy} and \frac{2\times 3x}{6xy} have the same denominator, add them by adding their numerators.

$$\frac{4}{\frac{4\times 2y+2\times 3x}{6xy}}$$

Do the multiplications in 4\times 2y+2\times 3x.

$$\frac{4}{\frac{8y+6x}{6xy}}$$

Factor the expressions that are not already factored in \frac{8y+6x}{6xy}.

$$\frac{4}{\frac{2\left(3x+4y\right)}{6xy}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{4}{\frac{3x+4y}{3xy}}$$

Divide 4 by \frac{3x+4y}{3xy} by multiplying 4 by the reciprocal of \frac{3x+4y}{3xy}.

$$\frac{4\times 3xy}{3x+4y}$$

Multiply 4 and 3 to get 12.

$$\frac{12xy}{3x+4y}$$

Differentiate w.r.t. x

$$48\times \left(\frac{y}{3x+4y}\right)^{2}$$