Solve 4(x)+5/5(x)+4*4(1/x)+5/5(frac{1{x})+4}

$$\frac{ 4(x)+5 }{ 5(x)+4 } \times \frac{ 4( \frac{ 1 }{ x } )+5 }{ 5( \frac{ 1 }{ x } )+4 }$$

Evaluate

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Solution Steps

Express 4\times \frac{1}{x} as a single fraction.

$$\frac{4x+5}{5x+4}\times \frac{\frac{4}{x}+5}{5\times \frac{1}{x}+4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{x}{x}.

$$\frac{4x+5}{5x+4}\times \frac{\frac{4}{x}+\frac{5x}{x}}{5\times \frac{1}{x}+4}$$

Since \frac{4}{x} and \frac{5x}{x} have the same denominator, add them by adding their numerators.

$$\frac{4x+5}{5x+4}\times \frac{\frac{4+5x}{x}}{5\times \frac{1}{x}+4}$$

Express 5\times \frac{1}{x} as a single fraction.

$$\frac{4x+5}{5x+4}\times \frac{\frac{4+5x}{x}}{\frac{5}{x}+4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x}{x}.

$$\frac{4x+5}{5x+4}\times \frac{\frac{4+5x}{x}}{\frac{5}{x}+\frac{4x}{x}}$$

Since \frac{5}{x} and \frac{4x}{x} have the same denominator, add them by adding their numerators.

$$\frac{4x+5}{5x+4}\times \frac{\frac{4+5x}{x}}{\frac{5+4x}{x}}$$

Divide \frac{4+5x}{x} by \frac{5+4x}{x} by multiplying \frac{4+5x}{x} by the reciprocal of \frac{5+4x}{x}.

$$\frac{4x+5}{5x+4}\times \frac{\left(4+5x\right)x}{x\left(5+4x\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{4x+5}{5x+4}\times \frac{5x+4}{4x+5}$$

Multiply \frac{4x+5}{5x+4} times \frac{5x+4}{4x+5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4x+5\right)\left(5x+4\right)}{\left(5x+4\right)\left(4x+5\right)}$$

Cancel out \left(4x+5\right)\left(5x+4\right) in both numerator and denominator.

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Factor

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