Question

Fraction numerator 5 x squared plus 6 x plus 1 over denominator x squared plus 7 x plus 6 end fraction divided by left parenthesis 5 x plus 1 right parenthesis

Answer 1

Answer:

The value of the expression is, $\frac{1}{x+6}$.

Step-by-step explanation:

The expression is as follows:

$\frac{5x^{2}+6x+1}{x^{2}+7x+6}\div (5x+1)$

Solve as follows:

$\frac{5x^{2}+6x+1}{x^{2}+7x+6}\div (5x+1)=\frac{5x^{2}+6x+1}{x^{2}+7x+6}\times \frac{1}{5x+1}$

                               $=\frac{5x^{2}+5x+x+1}{x^{2}+6x+x+6}\times\frac{1}{5x+1}\\\\=\frac{(5x+1)(x+1)}{(x+6)(x+1)}\times\frac{1}{5x+1}\\\\=\frac{1}{x+6}$

Thus, the value of the expression is, $\frac{1}{x+6}$.