Solve x/frac{y{z}+z/y}

$$\frac{ x }{ \frac{ y }{ z } + \frac{ z }{ y } }$$

Evaluate

$$\frac{xyz}{y^{2}+z^{2}}$$

Short Solution Steps

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

$$\frac{x}{\frac{yy}{yz}+\frac{zz}{yz}}$$

Since \frac{yy}{yz} and \frac{zz}{yz} have the same denominator, add them by adding their numerators.

$$\frac{x}{\frac{yy+zz}{yz}}$$

Do the multiplications in yy+zz.

$$\frac{x}{\frac{y^{2}+z^{2}}{yz}}$$

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

$$\frac{xyz}{y^{2}+z^{2}}$$

Differentiate w.r.t. x

$$\frac{yz}{y^{2}+z^{2}}$$