Solve 51^2-49^2/51^2+2*51*49+49^2

$$\frac{ { 51 }^{ 2 } - { 49 }^{ 2 } }{ { 51 }^{ 2 } +2 \times 51 \times 49+ { 49 }^{ 2 } }$$

Evaluate

$$\frac{1}{50}=0.02$$

Solution Steps

Calculate 51 to the power of 2 and get 2601.

$$\frac{2601-49^{2}}{51^{2}+2\times 51\times 49+49^{2}}$$

Calculate 49 to the power of 2 and get 2401.

$$\frac{2601-2401}{51^{2}+2\times 51\times 49+49^{2}}$$

Subtract 2401 from 2601 to get 200.

$$\frac{200}{51^{2}+2\times 51\times 49+49^{2}}$$

Calculate 51 to the power of 2 and get 2601.

$$\frac{200}{2601+2\times 51\times 49+49^{2}}$$

Multiply 2 and 51 to get 102.

$$\frac{200}{2601+102\times 49+49^{2}}$$

Multiply 102 and 49 to get 4998.

$$\frac{200}{2601+4998+49^{2}}$$

Add 2601 and 4998 to get 7599.

$$\frac{200}{7599+49^{2}}$$

Calculate 49 to the power of 2 and get 2401.

$$\frac{200}{7599+2401}$$

Add 7599 and 2401 to get 10000.

$$\frac{200}{10000}$$

Reduce the fraction \frac{200}{10000} to lowest terms by extracting and canceling out 200.

$$\frac{1}{50}$$

Factor

$$\frac{1}{2 \cdot 5 ^ {2}} = 0.02$$