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Simplify. Express your answer as a single fraction in simplest form. \newline54+2q4\frac{5}{4} + \frac{2}{q^4}

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Add and subtract rational expressionsright chevron icon

Full solution

Q. Simplify. Express your answer as a single fraction in simplest form. \newline54+2q4\frac{5}{4} + \frac{2}{q^4}
  1. Identify LCD: 54+2q4\frac{5}{4} + \frac{2}{q^4}\newlineIdentify the least common denominator (LCD) for the fractions.\newlineThe LCD for 44 and q4q^4 is 4q44q^4.
  2. Rewrite fractions: 54+2q4\frac{5}{4} + \frac{2}{q^4}\newlineRewrite each fraction with the common denominator 4q44q^4.\newline(5⋅q44⋅q4)+(2⋅4q4⋅4)(\frac{5 \cdot q^4}{4 \cdot q^4}) + (\frac{2 \cdot 4}{q^4 \cdot 4})\newline=5q44q4+84q4=\frac{5q^4}{4q^4} + \frac{8}{4q^4}
  3. Combine fractions: (5q44q4)+(84q4)(\frac{5q^4}{4q^4}) + (\frac{8}{4q^4})\newlineCombine the fractions over the common denominator.\newline(5q4+84q4)(\frac{5q^4 + 8}{4q^4})
  4. Check numerator: 5q4+84q4\frac{5q^4 + 8}{4q^4}\newlineCheck if the numerator can be simplified or factored further.\newlineThe numerator 5q4+85q^4 + 8 cannot be factored further, so the expression is already in its simplest form.

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