Question

1. simplify: \\(\frac{7v^2}{v + 9} div \frac{3v - 21}{7 - v}\\). teks a2.7(f)

a) \\(\frac{v + 6}{v - 5}\\)
b) \\(\frac{-7v^2}{3(v + 9)}\\)
c) \\(\frac{v + 3}{7v^2}\\)
d) \\(\frac{v^2 + 8}{v(v + 9)}\\)
\\(\bigcirc\\) b
\\(\bigcirc\\) a
\\(\bigcirc\\) c
\\(\bigcirc\\) d

Explanation:

Step1: Rewrite division as multiplication

To divide by a fraction, multiply by its reciprocal. So, \(\frac{7v^{2}}{v + 9}\div\frac{3v - 21}{7 - v}=\frac{7v^{2}}{v + 9}\times\frac{7 - v}{3v - 21}\)

Step2: Factor the expressions

Factor \(3v - 21\) as \(3(v - 7)\) and notice that \(7 - v=-(v - 7)\). So the expression becomes \(\frac{7v^{2}}{v + 9}\times\frac{-(v - 7)}{3(v - 7)}\)

Step3: Cancel common factors

Cancel out the common factor \((v - 7)\) from the numerator and the denominator. We get \(\frac{7v^{2}\times(- 1)}{(v + 9)\times3}=\frac{-7v^{2}}{3(v + 9)}\)

Answer:

B) \(\frac{-7v^{2}}{3(v + 9)}\)