Solve 53^2x-43^2x-1/23^2x+1-3^2x

$$\frac{ 5 { 3 }^{ 2x } -4 { 3 }^{ 2x-1 } }{ 2 { 3 }^{ 2x+1 } - { 3 }^{ 2x } }$$

Evaluate

$$\frac{11}{15}\approx 0.733333333$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{3}\left(15-4\right)\times \left(3^{x}\right)^{2}}{\left(6-1\right)\times \left(3^{x}\right)^{2}}$$

Cancel out \left(3^{x}\right)^{2} in both numerator and denominator.

$$\frac{\frac{1}{3}\left(15-4\right)}{6-1}$$

Subtract 4 from 15 to get 11.

$$\frac{\frac{1}{3}\times 11}{6-1}$$

Multiply \frac{1}{3} and 11 to get \frac{11}{3}.

$$\frac{\frac{11}{3}}{6-1}$$

Subtract 1 from 6 to get 5.

$$\frac{\frac{11}{3}}{5}$$

Express \frac{\frac{11}{3}}{5} as a single fraction.

$$\frac{11}{3\times 5}$$

Multiply 3 and 5 to get 15.

$$\frac{11}{15}$$

Factor

$$\frac{11}{3 \cdot 5} = 0.7333333333333333$$