Question

SIMPLIFYING RATIONAL EXPRESSIONS Simplify the expression. $$\frac{5}{4 x}-\frac{7}{3 x}$$

Short answer

The simplified form of the given expression is \( \frac{-13}{12x} \).

Step-by-step solution

Identifying the Expression

The given expression is \( \frac{5}{4 x} - \frac{7}{3 x} \). This is a rational expression since it consists of two rational fractions.

Identifying the Common Denominator

For combining the two fractions, we need a common denominator. The common denominator would be the product of \(4x\) and \(3x\) which is \(12x^2\).

Altering the Fractions to have the Common Denominator

We can express the fractions having \(12x^2\) as their denominator. To do this, we multiply top and bottom of \( \frac{5}{4x} \) by \(3x\) and \( \frac{7}{3x} \) by \(4x\). So, the altered expressions are \( \frac{15x}{12x^2} \) and \( \frac{28x}{12x^2} \) respectively.

Substituting the Fractions in the Expression

Now substitute these altered fractions into the given expression. \( \frac{15x}{12x^2} - \frac{28x}{12x^2} = \frac{15x-28x}{12x^2} = \frac{-13x}{12x^2} \).

Simplifying the Expression

Simplify the above expression by cancelling the \(x\) factor out from numerator and denominator to get \( \frac{-13}{12x} \). This is the final simplified expression.