Question

simplify.
\frac{\frac{3x + 21}{5}}{\frac{4x + 28}{35x}}

Explanation:

Step1: Rewrite as division of fractions

Dividing by a fraction is multiplying by its reciprocal, so \(\frac{\frac{3x + 21}{5}}{\frac{4x + 28}{35x}}=\frac{3x + 21}{5}\times\frac{35x}{4x + 28}\)

Step2: Factor numerators and denominators

Factor out common terms: \(3x + 21 = 3(x + 7)\), \(4x + 28 = 4(x + 7)\), and \(35x\) remains, \(5\) remains. So we have \(\frac{3(x + 7)}{5}\times\frac{35x}{4(x + 7)}\)

Step3: Cancel common factors

Cancel out \((x + 7)\) from numerator and denominator, and simplify \(\frac{35}{5}=7\). So we get \(\frac{3\times7x}{4}=\frac{21x}{4}\)

Answer:

\(\frac{21x}{4}\)