Solve 1/{left(frac{8{6}right)}^2}-1/{left(frac{7{6}right)}^2}=

$$\frac{ 1 }{ { \left( \frac{ 8 }{ 6 } \right) }^{ 2 } } - \frac{ 1 }{ { \left( \frac{ 7 }{ 6 } \right) }^{ 2 } } =$$

Evaluate

$$-\frac{135}{784}\approx -0.172193878$$

Solution Steps

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{\left(\frac{4}{3}\right)^{2}}-\frac{1}{\left(\frac{7}{6}\right)^{2}}$$

Calculate \frac{4}{3} to the power of 2 and get \frac{16}{9}.

$$\frac{1}{\frac{16}{9}}-\frac{1}{\left(\frac{7}{6}\right)^{2}}$$

Divide 1 by \frac{16}{9} by multiplying 1 by the reciprocal of \frac{16}{9}.

$$1\times \frac{9}{16}-\frac{1}{\left(\frac{7}{6}\right)^{2}}$$

Multiply 1 and \frac{9}{16} to get \frac{9}{16}.

$$\frac{9}{16}-\frac{1}{\left(\frac{7}{6}\right)^{2}}$$

Calculate \frac{7}{6} to the power of 2 and get \frac{49}{36}.

$$\frac{9}{16}-\frac{1}{\frac{49}{36}}$$

Divide 1 by \frac{49}{36} by multiplying 1 by the reciprocal of \frac{49}{36}.

$$\frac{9}{16}-1\times \frac{36}{49}$$

Multiply 1 and \frac{36}{49} to get \frac{36}{49}.

$$\frac{9}{16}-\frac{36}{49}$$

Subtract \frac{36}{49} from \frac{9}{16} to get -\frac{135}{784}.

$$-\frac{135}{784}$$

Factor

$$-\frac{135}{784} = -0.17219387755102042$$