Solve 6kg/frac{2kg{P}+4kg/p}

$$\frac { 6 k g } { \frac { 2 k g } { P } + \frac { 4 k g } { p } }$$

Evaluate

$$\frac{3Pp}{p+2P}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of P and p is Pp. Multiply \frac{2kg}{P} times \frac{p}{p}. Multiply \frac{4kg}{p} times \frac{P}{P}.

$$\frac{6kg}{\frac{2kgp}{Pp}+\frac{4kgP}{Pp}}$$

Since \frac{2kgp}{Pp} and \frac{4kgP}{Pp} have the same denominator, add them by adding their numerators.

$$\frac{6kg}{\frac{2kgp+4kgP}{Pp}}$$

Divide 6kg by \frac{2kgp+4kgP}{Pp} by multiplying 6kg by the reciprocal of \frac{2kgp+4kgP}{Pp}.

$$\frac{6kgPp}{2kgp+4kgP}$$

Factor the expressions that are not already factored.

$$\frac{6Pgkp}{2gk\left(p+2P\right)}$$

Cancel out 2gk in both numerator and denominator.

$$\frac{3Pp}{p+2P}$$

Differentiate w.r.t. P

$$3\times \left(\frac{p}{p+2P}\right)^{2}$$