Solve 2/6a^2bc^2-5/ac^2

$$\frac { 2 } { 6 a ^ { 2 } b c ^ { 2 } } - \frac { 5 } { a c ^ { 2 } }$$

Evaluate

$$\frac{1-15ab}{3b\left(ac\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6a^{2}bc^{2} and ac^{2} is 6ba^{2}c^{2}. Multiply \frac{5}{ac^{2}} times \frac{6ab}{6ab}.

$$\frac{2}{6ba^{2}c^{2}}-\frac{5\times 6ab}{6ba^{2}c^{2}}$$

Since \frac{2}{6ba^{2}c^{2}} and \frac{5\times 6ab}{6ba^{2}c^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-5\times 6ab}{6ba^{2}c^{2}}$$

Do the multiplications in 2-5\times 6ab.

$$\frac{2-30ab}{6ba^{2}c^{2}}$$

Factor the expressions that are not already factored in \frac{2-30ab}{6ba^{2}c^{2}}.

$$\frac{2\left(-15ab+1\right)}{6ba^{2}c^{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-15ab+1}{3ba^{2}c^{2}}$$

Factor

$$\frac{1-15ab}{3b\left(ac\right)^{2}}$$