23) $\frac{2n^{3}+12n^{2}-14n}{7n^{2}-14n + 7}$
23) $\frac{2n^{3}+12n^{2}-14n}{7n^{2}-14n + 7}$
Answer
Explanation:
Step1: Factor out the greatest - common factor from the numerator and denominator
The numerator (2n^{3}+12n^{2}-14n = 2n(n^{2}+6n - 7)). Factor (n^{2}+6n - 7=(n + 7)(n-1)), so the numerator is (2n(n + 7)(n - 1)). The denominator (7n^{2}-14n + 7=7(n^{2}-2n + 1)). Factor (n^{2}-2n + 1=(n - 1)^{2}), so the denominator is (7(n - 1)^{2}).
Step2: Simplify the rational expression
(\frac{2n(n + 7)(n - 1)}{7(n - 1)^{2}}=\frac{2n(n + 7)}{7(n - 1)}), for (n\neq1)
Answer:
(\frac{2n(n + 7)}{7(n - 1)},n\neq1)