Solve (9+1)^2/(9-1)^2*3a-5/29+2div9^2+9/9^2+9-2

$$\frac { ( 9 + 1 ) ^ { 2 } } { ( 9 - 1 ) ^ { 2 } } \cdot \frac { 3 a - 5 } { 29 + 2 } \div \frac { 9 ^ { 2 } + 9 } { 9 ^ { 2 } + 9 - 2 }$$

Evaluate

$$\frac{55a}{372}-\frac{275}{1116}$$

Solution Steps

Add 9 and 1 to get 10.

$$\frac{\frac{10^{2}}{\left(9-1\right)^{2}}\times \frac{3a-5}{29+2}}{\frac{9^{2}+9}{9^{2}+9-2}}$$

Calculate 10 to the power of 2 and get 100.

$$\frac{\frac{100}{\left(9-1\right)^{2}}\times \frac{3a-5}{29+2}}{\frac{9^{2}+9}{9^{2}+9-2}}$$

Subtract 1 from 9 to get 8.

$$\frac{\frac{100}{8^{2}}\times \frac{3a-5}{29+2}}{\frac{9^{2}+9}{9^{2}+9-2}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{\frac{100}{64}\times \frac{3a-5}{29+2}}{\frac{9^{2}+9}{9^{2}+9-2}}$$

Reduce the fraction \frac{100}{64} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{25}{16}\times \frac{3a-5}{29+2}}{\frac{9^{2}+9}{9^{2}+9-2}}$$

Add 29 and 2 to get 31.

$$\frac{\frac{25}{16}\times \frac{3a-5}{31}}{\frac{9^{2}+9}{9^{2}+9-2}}$$

Multiply \frac{25}{16} times \frac{3a-5}{31} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{25\left(3a-5\right)}{16\times 31}}{\frac{9^{2}+9}{9^{2}+9-2}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{\frac{25\left(3a-5\right)}{16\times 31}}{\frac{81+9}{9^{2}+9-2}}$$

Add 81 and 9 to get 90.

$$\frac{\frac{25\left(3a-5\right)}{16\times 31}}{\frac{90}{9^{2}+9-2}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{\frac{25\left(3a-5\right)}{16\times 31}}{\frac{90}{81+9-2}}$$

Add 81 and 9 to get 90.

$$\frac{\frac{25\left(3a-5\right)}{16\times 31}}{\frac{90}{90-2}}$$

Subtract 2 from 90 to get 88.

$$\frac{\frac{25\left(3a-5\right)}{16\times 31}}{\frac{90}{88}}$$

Reduce the fraction \frac{90}{88} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{25\left(3a-5\right)}{16\times 31}}{\frac{45}{44}}$$

Divide \frac{25\left(3a-5\right)}{16\times 31} by \frac{45}{44} by multiplying \frac{25\left(3a-5\right)}{16\times 31} by the reciprocal of \frac{45}{44}.

$$\frac{25\left(3a-5\right)\times 44}{16\times 31\times 45}$$

Cancel out 4\times 5 in both numerator and denominator.

$$\frac{5\times 11\left(3a-5\right)}{4\times 9\times 31}$$

Multiply 5 and 11 to get 55.

$$\frac{55\left(3a-5\right)}{4\times 9\times 31}$$

Multiply 4 and 9 to get 36.

$$\frac{55\left(3a-5\right)}{36\times 31}$$

Multiply 36 and 31 to get 1116.

$$\frac{55\left(3a-5\right)}{1116}$$

Use the distributive property to multiply 55 by 3a-5.

$$\frac{165a-275}{1116}$$

Expand

$$\frac{55a}{372}-\frac{275}{1116}$$

Solution Steps

Add 9 and 1 to get 10.

$$\frac{\frac{10^{2}}{\left(9-1\right)^{2}}\times \frac{3a-5}{29+2}}{\frac{9^{2}+9}{9^{2}+9-2}}$$

Calculate 10 to the power of 2 and get 100.

$$\frac{\frac{100}{\left(9-1\right)^{2}}\times \frac{3a-5}{29+2}}{\frac{9^{2}+9}{9^{2}+9-2}}$$

Subtract 1 from 9 to get 8.

$$\frac{\frac{100}{8^{2}}\times \frac{3a-5}{29+2}}{\frac{9^{2}+9}{9^{2}+9-2}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{\frac{100}{64}\times \frac{3a-5}{29+2}}{\frac{9^{2}+9}{9^{2}+9-2}}$$

Reduce the fraction \frac{100}{64} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{25}{16}\times \frac{3a-5}{29+2}}{\frac{9^{2}+9}{9^{2}+9-2}}$$

Add 29 and 2 to get 31.

$$\frac{\frac{25}{16}\times \frac{3a-5}{31}}{\frac{9^{2}+9}{9^{2}+9-2}}$$

Multiply \frac{25}{16} times \frac{3a-5}{31} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{25\left(3a-5\right)}{16\times 31}}{\frac{9^{2}+9}{9^{2}+9-2}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{\frac{25\left(3a-5\right)}{16\times 31}}{\frac{81+9}{9^{2}+9-2}}$$

Add 81 and 9 to get 90.

$$\frac{\frac{25\left(3a-5\right)}{16\times 31}}{\frac{90}{9^{2}+9-2}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{\frac{25\left(3a-5\right)}{16\times 31}}{\frac{90}{81+9-2}}$$

Add 81 and 9 to get 90.

$$\frac{\frac{25\left(3a-5\right)}{16\times 31}}{\frac{90}{90-2}}$$

Subtract 2 from 90 to get 88.

$$\frac{\frac{25\left(3a-5\right)}{16\times 31}}{\frac{90}{88}}$$

Reduce the fraction \frac{90}{88} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{25\left(3a-5\right)}{16\times 31}}{\frac{45}{44}}$$

Divide \frac{25\left(3a-5\right)}{16\times 31} by \frac{45}{44} by multiplying \frac{25\left(3a-5\right)}{16\times 31} by the reciprocal of \frac{45}{44}.

$$\frac{25\left(3a-5\right)\times 44}{16\times 31\times 45}$$

Cancel out 4\times 5 in both numerator and denominator.

$$\frac{5\times 11\left(3a-5\right)}{4\times 9\times 31}$$

Multiply 5 and 11 to get 55.

$$\frac{55\left(3a-5\right)}{4\times 9\times 31}$$

Multiply 4 and 9 to get 36.

$$\frac{55\left(3a-5\right)}{36\times 31}$$

Multiply 36 and 31 to get 1116.

$$\frac{55\left(3a-5\right)}{1116}$$

Use the distributive property to multiply 55 by 3a-5.

$$\frac{165a-275}{1116}$$