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