Solve [(3/2)^2-sqrt{2^2}*(-3/4)*5/2+(-1/2)^2]div(-frac{7}{4}+frac{1}{2})^2

$$[ ( \frac { 3 } { 2 } ) ^ { 2 } - \sqrt { 2 ^ { 2 } } \times ( - \frac { 3 } { 4 } ) \times \frac { 5 } { 2 } + ( - \frac { 1 } { 2 } ) ^ { 2 } ] \div ( - \frac { 7 } { 4 } + \frac { 1 } { 2 } ) ^ { 2 }$$

Evaluate

$$4$$

Solution Steps

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{\frac{9}{4}-\sqrt{2^{2}}\left(-\frac{3}{4}\right)\times \frac{5}{2}+\left(-\frac{1}{2}\right)^{2}}{\left(-\frac{7}{4}+\frac{1}{2}\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\frac{9}{4}-\sqrt{4}\left(-\frac{3}{4}\right)\times \frac{5}{2}+\left(-\frac{1}{2}\right)^{2}}{\left(-\frac{7}{4}+\frac{1}{2}\right)^{2}}$$

Calculate the square root of 4 and get 2.

$$\frac{\frac{9}{4}-2\left(-\frac{3}{4}\right)\times \frac{5}{2}+\left(-\frac{1}{2}\right)^{2}}{\left(-\frac{7}{4}+\frac{1}{2}\right)^{2}}$$

Multiply 2 and -\frac{3}{4} to get -\frac{3}{2}.

$$\frac{\frac{9}{4}-\left(-\frac{3}{2}\times \frac{5}{2}\right)+\left(-\frac{1}{2}\right)^{2}}{\left(-\frac{7}{4}+\frac{1}{2}\right)^{2}}$$

Multiply -\frac{3}{2} and \frac{5}{2} to get -\frac{15}{4}.

$$\frac{\frac{9}{4}-\left(-\frac{15}{4}\right)+\left(-\frac{1}{2}\right)^{2}}{\left(-\frac{7}{4}+\frac{1}{2}\right)^{2}}$$

The opposite of -\frac{15}{4} is \frac{15}{4}.

$$\frac{\frac{9}{4}+\frac{15}{4}+\left(-\frac{1}{2}\right)^{2}}{\left(-\frac{7}{4}+\frac{1}{2}\right)^{2}}$$

Add \frac{9}{4} and \frac{15}{4} to get 6.

$$\frac{6+\left(-\frac{1}{2}\right)^{2}}{\left(-\frac{7}{4}+\frac{1}{2}\right)^{2}}$$

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

$$\frac{6+\frac{1}{4}}{\left(-\frac{7}{4}+\frac{1}{2}\right)^{2}}$$

Add 6 and \frac{1}{4} to get \frac{25}{4}.

$$\frac{\frac{25}{4}}{\left(-\frac{7}{4}+\frac{1}{2}\right)^{2}}$$

Add -\frac{7}{4} and \frac{1}{2} to get -\frac{5}{4}.

$$\frac{\frac{25}{4}}{\left(-\frac{5}{4}\right)^{2}}$$

Calculate -\frac{5}{4} to the power of 2 and get \frac{25}{16}.

$$\frac{\frac{25}{4}}{\frac{25}{16}}$$

Divide \frac{25}{4} by \frac{25}{16} by multiplying \frac{25}{4} by the reciprocal of \frac{25}{16}.

$$\frac{25}{4}\times \frac{16}{25}$$

Multiply \frac{25}{4} and \frac{16}{25} to get 4.

$$4$$

Factor

$$2^{2}$$