Solve 6a/c-36a^2+c^2/6ac+c-36a/6a

$$\frac{ 6a }{ c } - \frac{ 36 { a }^{ 2 } + { c }^{ 2 } }{ 6ac } + \frac{ c-36a }{ 6a }$$

Evaluate

$$-6$$

Short Solution Steps

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

$$\frac{6a\times 6a}{6ac}-\frac{36a^{2}+c^{2}}{6ac}+\frac{c-36a}{6a}$$

Since \frac{6a\times 6a}{6ac} and \frac{36a^{2}+c^{2}}{6ac} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6a\times 6a-\left(36a^{2}+c^{2}\right)}{6ac}+\frac{c-36a}{6a}$$

Do the multiplications in 6a\times 6a-\left(36a^{2}+c^{2}\right).

$$\frac{36a^{2}-36a^{2}-c^{2}}{6ac}+\frac{c-36a}{6a}$$

Combine like terms in 36a^{2}-36a^{2}-c^{2}.

$$\frac{-c^{2}}{6ac}+\frac{c-36a}{6a}$$

Cancel out c in both numerator and denominator.

$$\frac{-c}{6a}+\frac{c-36a}{6a}$$

Since \frac{-c}{6a} and \frac{c-36a}{6a} have the same denominator, add them by adding their numerators.

$$\frac{-c+c-36a}{6a}$$

Combine like terms in -c+c-36a.

$$\frac{-36a}{6a}$$

Cancel out 6a in both numerator and denominator.

$$-6$$

Factor

$$-6$$