Question

Simplify the expression. $$\frac{3}{10 x}-\frac{1}{4 x^{2}}$$

Short answer

\(\frac{6x - 5}{20x^2}\)

Step-by-step solution

Identify Like Terms

In the given expression \(\frac{3}{10 x}-\frac{1}{4 x^{2}}\), there are no like terms to combine directly. The denominators of the fractions are similar but not the same.

Find Common Denominator

The fractions can be summed up if they have a common denominator. Identify the least common denominator (LCD) between \(10x\) and \(4x^2\). The LCD is the least common multiple of the two denominators which is \(20x^2\).

Rewrite Fractions with Common Denominator

Now, rewrite each term with the common denominator. Recast \(\frac{3}{10x}\) and \(\frac{1}{4x^2}\) into equivalent fractions such that their denominator is \(20x^2\). By multiplying the numerator and the denominator of the first fraction by \(2x\), it becomes \(\frac{6x}{20x^2}\). The second fraction becomes \(\frac{5}{20x^2}\) when multiplied by 5.

Subtract Fractions

Now that both fractions have the same denominator, they can be combined by subtracting the numerators: \(\frac{6x - 5}{20x^2}\)

Simplify Resulting Fraction

The resulting fraction can't be simplified any further. So, \(\frac{6x - 5}{20x^2}\) is the simplified form of the given expression.