Questions: Divide: (5x/8) + (15x^2/4) (Assume all denominators are nonzero)

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)
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Solution

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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: \[ \boxed{\frac{5x(6x + 1)}{8}} \]

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