Solve 6/30j+6*4j-1/16j^4-8j^3+j^2

$$\frac { 6 } { 30 j + 6 } \cdot \frac { 4 j - 1 } { 16 j ^ { 4 } - 8 j ^ { 3 } + j ^ { 2 } }$$

Evaluate

$$\frac{1}{\left(4j-1\right)\left(5j+1\right)j^{2}}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{4j-1}{16j^{4}-8j^{3}+j^{2}}.

$$\frac{6}{30j+6}\times \frac{4j-1}{j^{2}\left(4j-1\right)^{2}}$$

Cancel out 4j-1 in both numerator and denominator.

$$\frac{6}{30j+6}\times \frac{1}{\left(4j-1\right)j^{2}}$$

Multiply \frac{6}{30j+6} times \frac{1}{\left(4j-1\right)j^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6}{\left(30j+6\right)\left(4j-1\right)j^{2}}$$

Use the distributive property to multiply 30j+6 by 4j-1 and combine like terms.

$$\frac{6}{\left(120j^{2}-6j-6\right)j^{2}}$$

Use the distributive property to multiply 120j^{2}-6j-6 by j^{2}.

$$\frac{6}{120j^{4}-6j^{3}-6j^{2}}$$

Expand

$$\frac{1}{4\left(j-\frac{1}{4}\right)\left(5j+1\right)j^{2}}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{4j-1}{16j^{4}-8j^{3}+j^{2}}.

$$\frac{6}{30j+6}\times \frac{4j-1}{j^{2}\left(4j-1\right)^{2}}$$

Cancel out 4j-1 in both numerator and denominator.

$$\frac{6}{30j+6}\times \frac{1}{\left(4j-1\right)j^{2}}$$

Multiply \frac{6}{30j+6} times \frac{1}{\left(4j-1\right)j^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6}{\left(30j+6\right)\left(4j-1\right)j^{2}}$$

Use the distributive property to multiply 30j+6 by 4j-1 and combine like terms.

$$\frac{6}{\left(120j^{2}-6j-6\right)j^{2}}$$

Use the distributive property to multiply 120j^{2}-6j-6 by j^{2}.

$$\frac{6}{120j^{4}-6j^{3}-6j^{2}}$$