QuestionJuly 16, 2025

The expression (x+5)/(25x)div (x^2+12x+35)/(35x) simplifies to: (7)/(5x+?) The missing number is __ The solution is square

The expression (x+5)/(25x)div (x^2+12x+35)/(35x) simplifies to: (7)/(5x+?) The missing number is __ The solution is square
The expression (x+5)/(25x)div (x^2+12x+35)/(35x) simplifies to: (7)/(5x+?)
The missing number is __
The solution is square

Solution
4.7(310 votes)

Answer

7 Explanation 1. Simplify the division Rewrite the division as multiplication by the reciprocal: \[ \frac{x+5}{25x} \times \frac{35x}{x^2 + 12x + 35} \] 2. Factor the quadratic expression Factor \( x^2 + 12x + 35 \) as ( (x+5)(x+7) ). 3. Cancel common factors Cancel ( x+5 ) and ( x ) from numerator and denominator: \[ \frac{1}{25} \times \frac{35}{(x+7)} = \frac{35}{25(x+7)} \] 4. Simplify the fraction Simplify \( \frac{35}{25} \) to \( \frac{7}{5} \): \[ \frac{7}{5(x+7)} \]

Explanation

1. Simplify the division<br /> Rewrite the division as multiplication by the reciprocal: <br />\[ \frac{x+5}{25x} \times \frac{35x}{x^2 + 12x + 35} \]<br /><br />2. Factor the quadratic expression<br /> Factor \( x^2 + 12x + 35 \) as ( (x+5)(x+7) ).<br /><br />3. Cancel common factors<br /> Cancel ( x+5 ) and ( x ) from numerator and denominator:<br />\[ \frac{1}{25} \times \frac{35}{(x+7)} = \frac{35}{25(x+7)} \]<br /><br />4. Simplify the fraction<br /> Simplify \( \frac{35}{25} \) to \( \frac{7}{5} \):<br />\[ \frac{7}{5(x+7)} \]
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