Solve 0*2xleft(x^2+6right)/{left(x^2+4right)^frac{3{2}}}-frac{0*1xsqrt{x^2+4}}{{left(1+{left(2/xright)}^2right)}^2}

$$\frac{ 0 \cdot 2x \left( { x }^{ 2 } +6 \right) }{ { \left( { x }^{ 2 } +4 \right) }^{ \frac{ 3 }{ 2 } } } - \frac{ 0 \cdot 1x \sqrt{ { x }^{ 2 } +4 } }{ { \left(1+ { \left( \frac{ 2 }{ x } \right) }^{ 2 } \right) }^{ 2 } }$$

Evaluate

$$0$$

Short Solution Steps

Multiply 0 and 2 to get 0.

$$\frac{0x\left(x^{2}+6\right)}{\left(x^{2}+4\right)^{\frac{3}{2}}}-\frac{0\times 1x\sqrt{x^{2}+4}}{\left(1+\left(\frac{2}{x}\right)^{2}\right)^{2}}$$

Anything times zero gives zero.

$$\frac{0}{\left(x^{2}+4\right)^{\frac{3}{2}}}-\frac{0\times 1x\sqrt{x^{2}+4}}{\left(1+\left(\frac{2}{x}\right)^{2}\right)^{2}}$$

Multiply 0 and 1 to get 0.

$$\frac{0}{\left(x^{2}+4\right)^{\frac{3}{2}}}-\frac{0x\sqrt{x^{2}+4}}{\left(1+\left(\frac{2}{x}\right)^{2}\right)^{2}}$$

To raise \frac{2}{x} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{0}{\left(x^{2}+4\right)^{\frac{3}{2}}}-\frac{0x\sqrt{x^{2}+4}}{\left(1+\frac{2^{2}}{x^{2}}\right)^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{x^{2}}{x^{2}}.

$$\frac{0}{\left(x^{2}+4\right)^{\frac{3}{2}}}-\frac{0x\sqrt{x^{2}+4}}{\left(\frac{x^{2}}{x^{2}}+\frac{2^{2}}{x^{2}}\right)^{2}}$$

Since \frac{x^{2}}{x^{2}} and \frac{2^{2}}{x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{0}{\left(x^{2}+4\right)^{\frac{3}{2}}}-\frac{0x\sqrt{x^{2}+4}}{\left(\frac{x^{2}+2^{2}}{x^{2}}\right)^{2}}$$

Combine like terms in x^{2}+2^{2}.

$$\frac{0}{\left(x^{2}+4\right)^{\frac{3}{2}}}-\frac{0x\sqrt{x^{2}+4}}{\left(\frac{x^{2}+4}{x^{2}}\right)^{2}}$$

To raise \frac{x^{2}+4}{x^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{0}{\left(x^{2}+4\right)^{\frac{3}{2}}}-\frac{0x\sqrt{x^{2}+4}}{\frac{\left(x^{2}+4\right)^{2}}{\left(x^{2}\right)^{2}}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{0}{\left(x^{2}+4\right)^{\frac{3}{2}}}-\frac{0x\sqrt{x^{2}+4}}{\frac{\left(x^{2}+4\right)^{2}}{x^{4}}}$$

Divide 0x\sqrt{x^{2}+4} by \frac{\left(x^{2}+4\right)^{2}}{x^{4}} by multiplying 0x\sqrt{x^{2}+4} by the reciprocal of \frac{\left(x^{2}+4\right)^{2}}{x^{4}}.

$$\frac{0}{\left(x^{2}+4\right)^{\frac{3}{2}}}-\frac{0x\sqrt{x^{2}+4}x^{4}}{\left(x^{2}+4\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{0}{\left(x^{2}+4\right)^{\frac{3}{2}}}-\frac{0x^{5}\sqrt{x^{2}+4}}{\left(x^{2}+4\right)^{2}}$$

Factor the expressions that are not already factored in \frac{0x^{5}\sqrt{x^{2}+4}}{\left(x^{2}+4\right)^{2}}.

$$\frac{0}{\left(x^{2}+4\right)^{\frac{3}{2}}}-\frac{0}{\left(x^{2}+4\right)^{2}}$$

Cancel out \sqrt{x^{2}+4} in both numerator and denominator.

$$\frac{0}{\left(x^{2}+4\right)^{\frac{3}{2}}}-\frac{0}{\left(x^{2}+4\right)^{\frac{3}{2}}}$$

Subtract \frac{0}{\left(x^{2}+4\right)^{\frac{3}{2}}} from \frac{0}{\left(x^{2}+4\right)^{\frac{3}{2}}} to get 0.

$$0$$

Factor

$$0$$