Solve f(1/x) = (3 * 1/x + 4)/(1/x - 5) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$f(\frac{1}{x})=\frac{3\frac{1}{x}+4}{\frac{1}{x}-5}$$

Evaluate

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

Short Solution Steps

Express $3\times \frac{1}{x}$ as a single fraction.

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

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

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

Since $\frac{3}{x}$ and $\frac{4x}{x}$ have the same denominator, add them by adding their numerators.

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

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

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

Since $\frac{1}{x}$ and $\frac{5x}{x}$ have the same denominator, subtract them by subtracting their numerators.

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

Divide $\frac{3+4x}{x}$ by $\frac{1-5x}{x}$ by multiplying $\frac{3+4x}{x}$ by the reciprocal of $\frac{1-5x}{x}$.

$$\frac{\left(3+4x\right)x}{x\left(1-5x\right)}$$

Cancel out $x$ in both numerator and denominator.

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

Expand

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

Short Solution Steps

Express $3\times \frac{1}{x}$ as a single fraction.

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

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

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

Since $\frac{3}{x}$ and $\frac{4x}{x}$ have the same denominator, add them by adding their numerators.

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

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

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

Since $\frac{1}{x}$ and $\frac{5x}{x}$ have the same denominator, subtract them by subtracting their numerators.

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

Divide $\frac{3+4x}{x}$ by $\frac{1-5x}{x}$ by multiplying $\frac{3+4x}{x}$ by the reciprocal of $\frac{1-5x}{x}$.

$$\frac{\left(3+4x\right)x}{x\left(1-5x\right)}$$

Cancel out $x$ in both numerator and denominator.

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