Question

Evaluate the expression for the given value(s) of the variable(s). $$\frac{3 a-b}{a} \text { when } a=\frac{1}{3} \text { and } b=-3$$

Short answer

The evaluated expression equals 12.

Step-by-step solution

Substitution of values into the equation

Substitute \(a = \frac{1}{3}\) and \(b = -3\) into the given equation. This will give us \(\frac{3 (\frac{1}{3}) - (-3)}{\frac{1}{3}}\).

Simplifying the numerator

The numerator simplifies to \(3 \times \frac{1}{3} - (-3)\) = \(1 + 3\) = \(4\).

Simplifying the denominator

The denominator simplifies to \( \frac{1}{3}\).

Solve the equation

To find the solution, the numerator and denominator of the resulting fraction, \(\frac{4}{\frac{1}{3}}\), should be calculated. If you multiply the numerator by the reciprocal of the denominator it simplifies to \(4\times3 = 12\).