Solve 17/16k^4+49/64k^2+1/8/k^2+frac{1{4}}

$$\frac { \frac { 17 } { 16 } k ^ { 4 } + \frac { 49 } { 64 } k ^ { 2 } + \frac { 1 } { 8 } } { k ^ { 2 } + \frac { 1 } { 4 } }$$

Evaluate

$$\frac{17k^{2}}{16}+\frac{1}{2}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{64}\left(4k^{2}+1\right)\left(17k^{2}+8\right)}{\frac{1}{4}\left(4k^{2}+1\right)}$$

Cancel out 4k^{2}+1 in both numerator and denominator.

$$\frac{\frac{1}{64}\left(17k^{2}+8\right)}{\frac{1}{4}}$$

Expand the expression.

$$\frac{\frac{17}{64}k^{2}+\frac{1}{8}}{\frac{1}{4}}$$

Divide \frac{17}{64}k^{2}+\frac{1}{8} by \frac{1}{4} by multiplying \frac{17}{64}k^{2}+\frac{1}{8} by the reciprocal of \frac{1}{4}.

$$\left(\frac{17}{64}k^{2}+\frac{1}{8}\right)\times 4$$

Use the distributive property to multiply \frac{17}{64}k^{2}+\frac{1}{8} by 4.

$$\frac{17}{16}k^{2}+\frac{1}{2}$$

Expand

$$\frac{17k^{2}}{16}+\frac{1}{2}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{64}\left(4k^{2}+1\right)\left(17k^{2}+8\right)}{\frac{1}{4}\left(4k^{2}+1\right)}$$

Cancel out 4k^{2}+1 in both numerator and denominator.

$$\frac{\frac{1}{64}\left(17k^{2}+8\right)}{\frac{1}{4}}$$

Expand the expression.

$$\frac{\frac{17}{64}k^{2}+\frac{1}{8}}{\frac{1}{4}}$$

Divide \frac{17}{64}k^{2}+\frac{1}{8} by \frac{1}{4} by multiplying \frac{17}{64}k^{2}+\frac{1}{8} by the reciprocal of \frac{1}{4}.

$$\left(\frac{17}{64}k^{2}+\frac{1}{8}\right)\times 4$$

Use the distributive property to multiply \frac{17}{64}k^{2}+\frac{1}{8} by 4.

$$\frac{17}{16}k^{2}+\frac{1}{2}$$