Solve 6x^2div(4x/y+3y^2/2)

$$6 x ^ { 2 } \div ( \frac { 4 x } { y } + \frac { 3 y ^ { 2 } } { 2 } )$$

Evaluate

$$\frac{12yx^{2}}{8x+3y^{3}}$$

Short Solution Steps

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

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

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

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

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

$$\frac{6x^{2}}{\frac{8x+3y^{3}}{2y}}$$

Divide 6x^{2} by \frac{8x+3y^{3}}{2y} by multiplying 6x^{2} by the reciprocal of \frac{8x+3y^{3}}{2y}.

$$\frac{6x^{2}\times 2y}{8x+3y^{3}}$$

Multiply 6 and 2 to get 12.

$$\frac{12x^{2}y}{8x+3y^{3}}$$

Differentiate w.r.t. x

$$\frac{24xy\left(4x+3y^{3}\right)}{\left(8x+3y^{3}\right)^{2}}$$