which expression is equivalent to \\(\\frac{2n}{n + 4} + \\frac{7}{n - 1}\\) if no denominator equals…

which expression is equivalent to \\(\\frac{2n}{n + 4} + \\frac{7}{n - 1}\\) if no denominator equals zero?\\n\\na. \\(\\frac{2n^2 + 5n + 28}{(n + 4)(n - 1)}\\)\\n\\nb. \\(\\frac{2n^2 + 5n + 4}{(n + 4)(n - 1)}\\)\\n\\nc. \\(\\frac{2n^2 + 6n + 28}{(n + 4)(n - 1)}\\)\\n\\nd. \\(\\frac{2n^2 + 6n + 4}{(n + 4)(n - 1)}\\)

which expression is equivalent to \\(\\frac{2n}{n + 4} + \\frac{7}{n - 1}\\) if no denominator equals zero?\\n\\na. \\(\\frac{2n^2 + 5n + 28}{(n + 4)(n - 1)}\\)\\n\\nb. \\(\\frac{2n^2 + 5n + 4}{(n + 4)(n - 1)}\\)\\n\\nc. \\(\\frac{2n^2 + 6n + 28}{(n + 4)(n - 1)}\\)\\n\\nd. \\(\\frac{2n^2 + 6n + 4}{(n + 4)(n - 1)}\\)

Answer

Explanation:

Step1: Find a common denominator

The denominators are (n + 4) and (n - 1), so the common denominator is ((n + 4)(n - 1)).

Step2: Rewrite each fraction with the common denominator

For (\frac{2n}{n + 4}), multiply numerator and denominator by (n - 1): (\frac{2n(n - 1)}{(n + 4)(n - 1)}=\frac{2n^2-2n}{(n + 4)(n - 1)}) For (\frac{7}{n - 1}), multiply numerator and denominator by (n + 4): (\frac{7(n + 4)}{(n + 4)(n - 1)}=\frac{7n + 28}{(n + 4)(n - 1)})

Step3: Add the two fractions

(\frac{2n^2-2n}{(n + 4)(n - 1)}+\frac{7n + 28}{(n + 4)(n - 1)}=\frac{2n^2-2n + 7n + 28}{(n + 4)(n - 1)}) Simplify the numerator: (2n^2+5n + 28) So the equivalent expression is (\frac{2n^2+5n + 28}{(n + 4)(n - 1)})

Answer:

A. (\frac{2n^2 + 5n + 28}{(n + 4)(n - 1)})