Questions: Subtract as indicated. Express your answer in lowest terms. -(beta^3/14-1/(7 x))

Solution Steps

To subtract the given fractions, we need to find a common denominator. The denominators are \(14\) and \(7x\). The least common denominator (LCD) will be \(14x\). Convert each fraction to have this common denominator, perform the subtraction, and simplify the result if possible.

To subtract the fractions \(-\frac{\beta^3}{14}\) and \(\frac{1}{7x}\), we first need to find a common denominator. The denominators are \(14\) and \(7x\). The least common denominator (LCD) is \(14x\).

Convert each fraction to have the common denominator \(14x\):

• The first fraction \(-\frac{\beta^3}{14}\) is converted by multiplying the numerator and denominator by \(x\), resulting in \(-\frac{\beta^3 \cdot x}{14x}\).
• The second fraction \(\frac{1}{7x}\) is converted by multiplying the numerator and denominator by \(2\), resulting in \(\frac{2}{14x}\).

Subtract the converted fractions: \[ -\frac{\beta^3 \cdot x}{14x} - \frac{2}{14x} = \frac{-\beta^3 \cdot x - 2}{14x} \]

The expression \(\frac{-\beta^3 \cdot x - 2}{14x}\) is already in its simplest form since there are no common factors in the numerator and the denominator that can be further simplified.

Final Answer