Solve 5/2-55/left(5-2right)^2+6/2-6*5/left(6-2right)^2+frac{7}{2-7}

$$\frac{ 5 }{ 2-5 } \frac{ 5 }{ { \left(5-2 \right) }^{ 2 } } + \frac{ 6 }{ 2-6 } \times \frac{ 5 }{ { \left(6-2 \right) }^{ 2 } } + \frac{ 7 }{ 2-7 }$$

Evaluate

$$-\frac{12073}{4320}\approx -2.794675926$$

Solution Steps

Subtract 5 from 2 to get -3.

$$\frac{5}{-3}\times \frac{5}{\left(5-2\right)^{2}}+\frac{6}{2-6}\times \frac{5}{\left(6-2\right)^{2}}+\frac{7}{2-7}$$

Fraction \frac{5}{-3} can be rewritten as -\frac{5}{3} by extracting the negative sign.

$$-\frac{5}{3}\times \frac{5}{\left(5-2\right)^{2}}+\frac{6}{2-6}\times \frac{5}{\left(6-2\right)^{2}}+\frac{7}{2-7}$$

Subtract 2 from 5 to get 3.

$$-\frac{5}{3}\times \frac{5}{3^{2}}+\frac{6}{2-6}\times \frac{5}{\left(6-2\right)^{2}}+\frac{7}{2-7}$$

Calculate 3 to the power of 2 and get 9.

$$-\frac{5}{3}\times \frac{5}{9}+\frac{6}{2-6}\times \frac{5}{\left(6-2\right)^{2}}+\frac{7}{2-7}$$

Multiply -\frac{5}{3} and \frac{5}{9} to get -\frac{25}{27}.

$$-\frac{25}{27}+\frac{6}{2-6}\times \frac{5}{\left(6-2\right)^{2}}+\frac{7}{2-7}$$

Subtract 6 from 2 to get -4.

$$-\frac{25}{27}+\frac{6}{-4}\times \frac{5}{\left(6-2\right)^{2}}+\frac{7}{2-7}$$

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

$$-\frac{25}{27}-\frac{3}{2}\times \frac{5}{\left(6-2\right)^{2}}+\frac{7}{2-7}$$

Subtract 2 from 6 to get 4.

$$-\frac{25}{27}-\frac{3}{2}\times \frac{5}{4^{2}}+\frac{7}{2-7}$$

Calculate 4 to the power of 2 and get 16.

$$-\frac{25}{27}-\frac{3}{2}\times \frac{5}{16}+\frac{7}{2-7}$$

Multiply -\frac{3}{2} and \frac{5}{16} to get -\frac{15}{32}.

$$-\frac{25}{27}-\frac{15}{32}+\frac{7}{2-7}$$

Subtract \frac{15}{32} from -\frac{25}{27} to get -\frac{1205}{864}.

$$-\frac{1205}{864}+\frac{7}{2-7}$$

Subtract 7 from 2 to get -5.

$$-\frac{1205}{864}+\frac{7}{-5}$$

Fraction \frac{7}{-5} can be rewritten as -\frac{7}{5} by extracting the negative sign.

$$-\frac{1205}{864}-\frac{7}{5}$$

Subtract \frac{7}{5} from -\frac{1205}{864} to get -\frac{12073}{4320}.

$$-\frac{12073}{4320}$$

Factor

$$-\frac{12073}{4320} = -2\frac{3433}{4320} = -2.794675925925926$$