Solve 1/sqrt{frac{16{9}}-1}

$$\frac{ 1 }{ \sqrt{ \frac{ 16 }{ 9 } } -1 }$$

Evaluate

$$3$$

Solution Steps

Rewrite the square root of the division \frac{16}{9} as the division of square roots \frac{\sqrt{16}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{1}{\frac{4}{3}-1}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{1}{\frac{4}{3}-\frac{3}{3}}$$

Since \frac{4}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{4-3}{3}}$$

Subtract 3 from 4 to get 1.

$$\frac{1}{\frac{1}{3}}$$

Divide 1 by \frac{1}{3} by multiplying 1 by the reciprocal of \frac{1}{3}.

$$1\times 3$$

Multiply 1 and 3 to get 3.

$$3$$

Factor

$$3$$