Question

Simplify the difference. n^2-10n+24/n^2-13n+42-9/n-7

Answer 1

-17n+12 is the answer

Answer 2

Answer:

Find the difference of : $\frac{n^2-10n+24}{n^2-13n+42} -\frac{9}{n-7}$

First Factorize the equation:

$n^2-10n+24$ as

$n^2-6n-4n+24$

$n(n-6)-4(n-6)$

$(n-6)(n-4)$

Similarly for

$n^2-13n+42$ as

$n^2-6n-7n+42$

$n(n-6)-7(n-6)$

$(n-6)(n-7)$

then;

$\frac{n^2-10n+24}{n^2-13n+42} -\frac{9}{n-7}$

$\frac{(n-6)(n-4)}{(n-6)(n-7)} -\frac{9}{n-7}$

Simplify:

$\frac{(n-4)}{(n-7)} -\frac{9}{n-7}$

then;

$\frac{n-4-9}{n-7} =\frac{n-13}{n-7}$

therefore, the simplified difference of $\frac{n^2-10n+24}{n^2-13n+42} -\frac{9}{n-7}$ is $\frac{n-13}{n-7}$