Simplify the expression (6x+8)/4 ÷ (x2+3)/(5x2) as a single fraction.

August 3, 2026Mathematics

$Simplify the expression (6x+8)/4 ÷ (x2+3)/(5x2) as a single fraction.$

ScanSolve AI Answer

August 3, 2026

Answer

$\frac{5x^2(3x+4)}{2(x^2+3)}$

Here's how to simplify the expression:

Step 1: To divide by a fraction, multiply by its reciprocal. $\frac{6x+8}{4} \div \frac{x^2+3}{5x^2} = \frac{6x+8}{4} \times \frac{5x^2}{x^2+3}$

Step 2: Multiply the numerators and the denominators. $\frac{(6x+8) \cdot 5x^2}{4 \cdot (x^2+3)}$

Step 3: Factor out common terms from the numerator. Notice that $6x+8$ can be factored as $2(3x+4)$ . $\frac{2(3x+4) \cdot 5x^2}{4(x^2+3)}$

Step 4: Simplify the numerical coefficients. The 2 in the numerator and the 4 in the denominator can be simplified. $\frac{10x^2(3x+4)}{4(x^2+3)} = \frac{5x^2(3x+4)}{2(x^2+3)}$ The expression cannot be simplified further.

The simplified expression is: $\frac{5x^2(3x+4){2(x^2+3)}}$ That's 2 down. 3 left today — send the next one.

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Quick Answer

Here's how to simplify the expression: Step 1: To divide by a fraction, multiply by its reciprocal.

Asked on August 3, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on August 3, 2026

Here's how to simplify the expression: Step 1: To divide by a fraction, multiply by its reciprocal. (6x+8)/(4) ÷ (x^2+3)/(5x^2) = (6x+8)/(4) × (5x^2)/(x^2+3) Step 2: Multiply the numerators and the denominators. ((6x+8) · 5x^2)/(4 · (x^2+3)) Step 3: Factor out common terms from the numerator. Notice that 6x+8 can be factored as 2(3x+4). (2(3x+4) · 5x^2)/(4(x^2+3)) Step 4: Simplify the numerical coefficients. The 2 in the numerator and the 4 in the denominator can be simplified. (10x^2(3x+4))/(4(x^2+3)) = (5x^2(3x+4))/(2(x^2+3)) The expression cannot be simplified further. The simplified expression is: (5x^2(3x+4))/(2(x^2+3)) That's 2 down. 3 left today — send the next one.

Asked on August 3, 2026Mathematics

ScanSolve AI AnswerAnswered on August 3, 2026

Here's how to simplify the expression: Step 1: To divide by a fraction, multiply by its reciprocal. (6x+8)/(4) ÷ (x^2+3)/(5x^2) = (6x+8)/(4) × (5x^2)/(x^2+3) Step 2: Multiply the numerators and the denominators. ((6x+8) · 5x^2)/(4 · (x^2+3)) Step 3: Factor out common terms from the numerator. Notice that 6x+8 can be factored as 2(3x+4). (2(3x+4) · 5x^2)/(4(x^2+3)) Step 4: Simplify the numerical coefficients. The 2 in the numerator and the 4 in the denominator can be simplified. (10x^2(3x+4))/(4(x^2+3)) = (5x^2(3x+4))/(2(x^2+3)) The expression cannot be simplified further. The simplified expression is: (5x^2(3x+4))/(2(x^2+3)) That's 2 down. 3 left today — send the next one.