Solve =f(x^2+6^2)/sqrt{4+36}

$$= \frac { f ( x ^ { 2 } + 6 ^ { 2 } ) } { \sqrt { 4 + 36 } }$$

Factor

$$\frac{\sqrt{10}f\left(x^{2}+36\right)}{20}$$

Solution Steps

Calculate 6 to the power of 2 and get 36.

$$factor(\frac{f\left(x^{2}+36\right)}{\sqrt{4+36}})$$

Add 4 and 36 to get 40.

$$factor(\frac{f\left(x^{2}+36\right)}{\sqrt{40}})$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$factor(\frac{f\left(x^{2}+36\right)}{2\sqrt{10}})$$

Rationalize the denominator of \frac{f\left(x^{2}+36\right)}{2\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$factor(\frac{f\left(x^{2}+36\right)\sqrt{10}}{2\left(\sqrt{10}\right)^{2}})$$

The square of \sqrt{10} is 10.

$$factor(\frac{f\left(x^{2}+36\right)\sqrt{10}}{2\times 10})$$

Multiply 2 and 10 to get 20.

$$factor(\frac{f\left(x^{2}+36\right)\sqrt{10}}{20})$$

Use the distributive property to multiply f by x^{2}+36.

$$factor(\frac{\left(fx^{2}+36f\right)\sqrt{10}}{20})$$

Use the distributive property to multiply fx^{2}+36f by \sqrt{10}.

$$factor(\frac{fx^{2}\sqrt{10}+36f\sqrt{10}}{20})$$

Consider fx^{2}\sqrt{10}+36f\sqrt{10}. Factor out f\sqrt{10}.

$$f\sqrt{10}\left(x^{2}+36\right)$$

Rewrite the complete factored expression. Polynomial x^{2}+36 is not factored since it does not have any rational roots.

$$\frac{f\left(x^{2}+36\right)\sqrt{10}}{20}$$

Evaluate

$$\frac{\sqrt{10}f\left(x^{2}+36\right)}{20}$$