Solve (5/4z^5-1/4z^4+3z^2+z-1/4)div(z^2-1/4)=

$$( \frac { 5 } { 4 } z ^ { 5 } - \frac { 1 } { 4 } z ^ { 4 } + 3 z ^ { 2 } + z - \frac { 1 } { 4 } ) \div ( z ^ { 2 } - \frac { 1 } { 4 } ) =$$

Evaluate

$$\frac{5z^{5}-z^{4}+12z^{2}+4z-1}{4z^{2}-1}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{4}\left(5z^{5}-z^{4}+12z^{2}+4z-1\right)}{\frac{1}{4}\left(2z-1\right)\left(2z+1\right)}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{5z^{5}-z^{4}+12z^{2}+4z-1}{\left(\frac{1}{4}\right)^{0}\left(2z-1\right)\left(2z+1\right)}$$

Expand the expression.

$$\frac{5z^{5}-z^{4}+12z^{2}+4z-1}{4z^{2}-1}$$

Expand

$$\frac{5z^{5}-z^{4}+12z^{2}+4z-1}{4z^{2}-1}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{4}\left(5z^{5}-z^{4}+12z^{2}+4z-1\right)}{\frac{1}{4}\left(2z-1\right)\left(2z+1\right)}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{5z^{5}-z^{4}+12z^{2}+4z-1}{\left(\frac{1}{4}\right)^{0}\left(2z-1\right)\left(2z+1\right)}$$

Expand the expression.

$$\frac{5z^{5}-z^{4}+12z^{2}+4z-1}{4z^{2}-1}$$