Solve (-a^5b^2c^4+frac{2/3a^5{b}^{2}{c}^{4}+5/6{a}^{5}{b}^{2}{c}^4}{-5/4{a}^3{b}^2{c}^3}

$$\frac{ (- { a }^{ 5 } { b }^{ 2 } { c }^{ 4 } + \frac{ 2 }{ 3 } { a }^{ 5 } { b }^{ 2 } { c }^{ 4 } + \frac{ 5 }{ 6 } { a }^{ 5 } { b }^{ 2 } { c }^{ 4 } }{ - \frac{ 5 }{ 4 } { a }^{ 3 } { b }^{ 2 } { c }^{ 3 } }$$

Evaluate

$$-\frac{2ca^{2}}{5}$$

Short Solution Steps

Combine \frac{2}{3}a^{5}b^{2}c^{4} and \frac{5}{6}a^{5}b^{2}c^{4} to get \frac{3}{2}a^{5}b^{2}c^{4}.

$$\frac{\left(-a^{5}\right)b^{2}c^{4}+\frac{3}{2}a^{5}b^{2}c^{4}}{-\frac{5}{4}a^{3}b^{2}c^{3}}$$

Factor the expressions that are not already factored.

$$\frac{\frac{1}{2}\left(3-2\right)b^{2}c^{4}a^{5}}{-\frac{5}{4}b^{2}a^{3}c^{3}}$$

Cancel out b^{2}a^{3}c^{3} in both numerator and denominator.

$$\frac{\frac{1}{2}\left(3-2\right)ca^{2}}{-\frac{5}{4}}$$

Expand the expression.

$$\frac{\frac{1}{2}ca^{2}}{-\frac{5}{4}}$$

Divide \frac{1}{2}ca^{2} by -\frac{5}{4} by multiplying \frac{1}{2}ca^{2} by the reciprocal of -\frac{5}{4}.

$$\frac{\frac{1}{2}ca^{2}\times 4}{-5}$$

Multiply \frac{1}{2} and 4 to get 2.

$$\frac{2ca^{2}}{-5}$$

Expand

$$-\frac{2ca^{2}}{5}$$

Short Solution Steps

Combine \frac{2}{3}a^{5}b^{2}c^{4} and \frac{5}{6}a^{5}b^{2}c^{4} to get \frac{3}{2}a^{5}b^{2}c^{4}.

$$\frac{\left(-a^{5}\right)b^{2}c^{4}+\frac{3}{2}a^{5}b^{2}c^{4}}{-\frac{5}{4}a^{3}b^{2}c^{3}}$$

Factor the expressions that are not already factored.

$$\frac{\frac{1}{2}\left(3-2\right)b^{2}c^{4}a^{5}}{-\frac{5}{4}b^{2}a^{3}c^{3}}$$

Cancel out b^{2}a^{3}c^{3} in both numerator and denominator.

$$\frac{\frac{1}{2}\left(3-2\right)ca^{2}}{-\frac{5}{4}}$$

Expand the expression.

$$\frac{\frac{1}{2}ca^{2}}{-\frac{5}{4}}$$

Divide \frac{1}{2}ca^{2} by -\frac{5}{4} by multiplying \frac{1}{2}ca^{2} by the reciprocal of -\frac{5}{4}.

$$\frac{\frac{1}{2}ca^{2}\times 4}{-5}$$

Multiply \frac{1}{2} and 4 to get 2.

$$\frac{2ca^{2}}{-5}$$