Solve frac{36a^{7}b^{5}c^{3}}{40ab^{3}c^{2}}+27a^3b^5c^8/44abc^2

$$\frac { 36 a ^ { 7 } b ^ { 5 } c ^ { 3 } } { 40 a b ^ { 3 } c ^ { 2 } } + \frac { 27 a ^ { 3 } b ^ { 5 } c ^ { 8 } } { 44 a b c ^ { 2 } }$$

Factor

$$\frac{9ca^{2}b^{2}\left(22a^{4}+15b^{2}c^{5}\right)}{220}$$

Solution Steps

Cancel out 4ac^{2}b^{3} in both numerator and denominator.

$$factor(\frac{9cb^{2}a^{6}}{10}+\frac{27a^{3}b^{5}c^{8}}{44abc^{2}})$$

Cancel out abc^{2} in both numerator and denominator.

$$factor(\frac{9cb^{2}a^{6}}{10}+\frac{27a^{2}b^{4}c^{6}}{44})$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10 and 44 is 220. Multiply \frac{9cb^{2}a^{6}}{10} times \frac{22}{22}. Multiply \frac{27a^{2}b^{4}c^{6}}{44} times \frac{5}{5}.

$$factor(\frac{22\times 9cb^{2}a^{6}}{220}+\frac{5\times 27a^{2}b^{4}c^{6}}{220})$$

Since \frac{22\times 9cb^{2}a^{6}}{220} and \frac{5\times 27a^{2}b^{4}c^{6}}{220} have the same denominator, add them by adding their numerators.

$$factor(\frac{22\times 9cb^{2}a^{6}+5\times 27a^{2}b^{4}c^{6}}{220})$$

Do the multiplications in 22\times 9cb^{2}a^{6}+5\times 27a^{2}b^{4}c^{6}.

$$factor(\frac{198cb^{2}a^{6}+135a^{2}b^{4}c^{6}}{220})$$

Consider 198cb^{2}a^{6}+135a^{2}b^{4}c^{6}. Factor out 9.

$$9\left(22cb^{2}a^{6}+15a^{2}b^{4}c^{6}\right)$$

Consider 22cb^{2}a^{6}+15a^{2}b^{4}c^{6}. Factor out cb^{2}a^{2}.

$$cb^{2}a^{2}\left(22a^{4}+15b^{2}c^{5}\right)$$

Rewrite the complete factored expression. Simplify.

$$\frac{9c\left(22a^{4}+15b^{2}c^{5}\right)a^{2}b^{2}}{220}$$

Evaluate

$$\frac{9c\left(ab\right)^{2}\left(22a^{4}+15b^{2}c^{5}\right)}{220}$$