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

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

Evaluate

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

Solution Steps

Cancel out 4 and 4.

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

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

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

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

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

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

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

Multiply 6 and 2 to get 12.

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

Differentiate w.r.t. x

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