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Simplify. Express your answer as a single fraction in simplest form.
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Q. Simplify. Express your answer as a single fraction in simplest form.
- Identify LCD: Identify the least common denominator (LCD) for the fractions.The denominators are and . The LCD for these two numbers is because it is the smallest number that both and can divide into without leaving a remainder.
- Rewrite with LCD: Rewrite each fraction with the common denominator of . To convert the first fraction, , to have a denominator of , multiply both the numerator and the denominator by . For the second fraction, , multiply both the numerator and the denominator by . \[\left(\frac{\(9\)q}{\(5\)}\right) \cdot \left(\frac{\(2\)}{\(2\)}\right) + \left(\frac{\(3\)qr}{\(2\)}\right) \cdot \left(\frac{\(5\)}{\(5\)}\right) = \frac{\(18\)q}{\(10\)} + \frac{\(15\)qr}{\(10\)}
- Combine fractions: Combine the fractions now that they have the same denominator. \(\newline\)\((18q + 15qr) / 10\)
- Factor out q: Factor out the common factor q from the numerator. \(q(18 + 15r) / 10\)
- Check for simplification: Check if the expression can be simplified further.\(\newline\)The expression \(q(18 + 15r) / 10\) is already in its simplest form. There are no common factors between the numerator and the denominator that can be canceled out.
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