Simplify (x^(2)+6x+8)/(8x)÷(x+4)/(12)

Factorize numerator: Factor the numerator of the first fraction. We need to factor the quadratic expression x^2 + 6x + 8. This can be factored into (x + 2)(x + 4). So, (x^2 + 6x + 8)/(8x) becomes ((x + 2)(x + 4))/(8x).Rewrite as reciprocal: Rewrite the division as multiplication by the reciprocal. The expression (x^(2)+6x+8)/(8x) ÷ (x+4)/(12) can be rewritten as ((x + 2)(x + 4))/(8x) * (12)/(x+4).Cancel common factors: Cancel out common factors. We can cancel the (x + 4) term in the numerator of the first fraction and the denominator of the second fraction. This gives us ((x + 2) * 12)/(8x).Simplify expression: Simplify the expression. Now we simplify ((x + 2) * 12)/(8x) by dividing both the numerator and the denominator by 4. This gives us (3(x + 2))/(2x).Distribute 3: Distribute the 3 in the numerator. Multiplying 3 by each term in the numerator gives us (3x + 6)/(2x).

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Algebra 2

Divide polynomials using long division

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Q. Simplify

\frac{x^{2}+6x+8}{8x} \div \frac{x+4}{12}

Factorize numerator: Factor the numerator of the first fraction. $\newline$ We need to factor the quadratic expression $x^2 + 6x + 8$ . $\newline$ This can be factored into $(x + 2)(x + 4)$ . $\newline$ So, $(x^2 + 6x + 8)/(8x)$ becomes $((x + 2)(x + 4))/(8x)$ .
Rewrite as reciprocal: Rewrite the division as multiplication by the reciprocal. $\newline$ The expression $(x^{2}+6x+8)/(8x) \div (x+4)/(12)$ can be rewritten as $((x + 2)(x + 4))/(8x) \times (12)/(x+4)$ .
Cancel common factors: Cancel out common factors. $\newline$ We can cancel the $(x + 4)$ term in the numerator of the first fraction and the denominator of the second fraction. $\newline$ This gives us $\frac{(x + 2) \times 12}{8x}$ .
Simplify expression: Simplify the expression. $\newline$ Now we simplify $((x + 2) \times 12)/(8x)$ by dividing both the numerator and the denominator by $4$ . $\newline$ This gives us $(3(x + 2))/(2x)$ .
Distribute $3$ : Distribute the $3$ in the numerator. Multiplying $3$ by each term in the numerator gives us $(3x + 6)/(2x)$ .