Questions: Divide: (5x/8) + (15x^2/4)
(Assume all denominators are nonzero)
Transcript text: Divide: $\frac{5 x}{8}+\frac{15 x^{2}}{4}$
(Assume all denominators are nonzero)
Solution
Solution Steps
To divide the given expression, we need to simplify it by combining like terms and then performing the division. Since the expression is a sum of fractions, we should first find a common denominator and then simplify.
Step 1: Define the Expression
We start with the given expression:
\[
\frac{5x}{8} + \frac{15x^2}{4}
\]
Step 2: Find a Common Denominator
To combine the fractions, we need a common denominator. The least common multiple of 8 and 4 is 8. Rewrite the second term with the common denominator:
\[
\frac{5x}{8} + \frac{15x^2 \cdot 2}{4 \cdot 2} = \frac{5x}{8} + \frac{30x^2}{8}
\]
Step 3: Combine the Fractions
Now that both fractions have the same denominator, we can combine them:
\[
\frac{5x + 30x^2}{8}
\]
Step 4: Factor the Numerator
Factor out the common term \(5x\) from the numerator:
\[
\frac{5x(6x + 1)}{8}
\]
Final Answer
The simplified form of the given expression is:
\[
\boxed{\frac{5x(6x + 1)}{8}}
\]