Solve (6/4x+10/4x)^-2/(frac{20{5}x)^-2}+2

$$\frac { ( \frac { 6 } { 4 } x + \frac { 10 } { 4 } x ) ^ { - 2 } } { ( \frac { 20 } { 5 } x ) ^ { - 2 } } + 2$$

Evaluate

$$3$$

Solution Steps

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\left(\frac{3}{2}x+\frac{10}{4}x\right)^{-2}}{\left(\frac{20}{5}x\right)^{-2}}+2$$

Reduce the fraction \frac{10}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\left(\frac{3}{2}x+\frac{5}{2}x\right)^{-2}}{\left(\frac{20}{5}x\right)^{-2}}+2$$

Combine \frac{3}{2}x and \frac{5}{2}x to get 4x.

$$\frac{\left(4x\right)^{-2}}{\left(\frac{20}{5}x\right)^{-2}}+2$$

Expand \left(4x\right)^{-2}.

$$\frac{4^{-2}x^{-2}}{\left(\frac{20}{5}x\right)^{-2}}+2$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{\frac{1}{16}x^{-2}}{\left(\frac{20}{5}x\right)^{-2}}+2$$

Divide 20 by 5 to get 4.

$$\frac{\frac{1}{16}x^{-2}}{\left(4x\right)^{-2}}+2$$

Expand \left(4x\right)^{-2}.

$$\frac{\frac{1}{16}x^{-2}}{4^{-2}x^{-2}}+2$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{\frac{1}{16}x^{-2}}{\frac{1}{16}x^{-2}}+2$$

Cancel out x^{-2} in both numerator and denominator.

$$\frac{\frac{1}{16}}{\frac{1}{16}}+2$$

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

$$\frac{1}{\left(\frac{1}{16}\right)^{0}}+2$$

Calculate \frac{1}{16} to the power of 0 and get 1.

$$\frac{1}{1}+2$$

Anything divided by one gives itself.

$$1+2$$

Add 1 and 2 to get 3.

$$3$$

Factor

$$3$$