Solve m+n/2mm-n/5m^3n1/10n^2=

$$\frac { m + n } { 2 m } \frac { m - n } { 5 m ^ { 3 } n } \frac { 1 } { 10 n ^ { 2 } } =$$

Evaluate

$$\frac{m^{2}-n^{2}}{100n^{3}m^{4}}$$

Short Solution Steps

Multiply \frac{m+n}{2m} times \frac{m-n}{5m^{3}n} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(m+n\right)\left(m-n\right)}{2m\times 5m^{3}n}\times \frac{1}{10n^{2}}$$

Multiply \frac{\left(m+n\right)\left(m-n\right)}{2m\times 5m^{3}n} times \frac{1}{10n^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(m+n\right)\left(m-n\right)}{2m\times 5m^{3}n\times 10n^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{\left(m+n\right)\left(m-n\right)}{2m^{4}\times 5n\times 10n^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\left(m+n\right)\left(m-n\right)}{2m^{4}\times 5n^{3}\times 10}$$

Multiply 2 and 5 to get 10.

$$\frac{\left(m+n\right)\left(m-n\right)}{10m^{4}n^{3}\times 10}$$

Multiply 10 and 10 to get 100.

$$\frac{\left(m+n\right)\left(m-n\right)}{100m^{4}n^{3}}$$

Consider \left(m+n\right)\left(m-n\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{m^{2}-n^{2}}{100m^{4}n^{3}}$$

Expand

$$-\frac{n^{2}-m^{2}}{100n^{3}m^{4}}$$

Short Solution Steps

Multiply \frac{m+n}{2m} times \frac{m-n}{5m^{3}n} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(m+n\right)\left(m-n\right)}{2m\times 5m^{3}n}\times \frac{1}{10n^{2}}$$

Multiply \frac{\left(m+n\right)\left(m-n\right)}{2m\times 5m^{3}n} times \frac{1}{10n^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(m+n\right)\left(m-n\right)}{2m\times 5m^{3}n\times 10n^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{\left(m+n\right)\left(m-n\right)}{2m^{4}\times 5n\times 10n^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\left(m+n\right)\left(m-n\right)}{2m^{4}\times 5n^{3}\times 10}$$

Multiply 2 and 5 to get 10.

$$\frac{\left(m+n\right)\left(m-n\right)}{10m^{4}n^{3}\times 10}$$

Multiply 10 and 10 to get 100.

$$\frac{\left(m+n\right)\left(m-n\right)}{100m^{4}n^{3}}$$

Consider \left(m+n\right)\left(m-n\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{m^{2}-n^{2}}{100m^{4}n^{3}}$$