Simplify (n^4-11n^2+30)/(n^4-7n^2+10)

$\frac{n^{4} - 11 n^{2} + 30}{n^{4} - 7 n^{2} + 10}$

Step 1

Simplify the numerator.

Rewrite $n^{4}$ as ${(n^{2})}^{2}$ .

$\frac{{(n^{2})}^{2} - 11 n^{2} + 30}{n^{4} - 7 n^{2} + 10}$

Let $u = n^{2}$ . Substitute $u$ for all occurrences of $n^{2}$ .

$\frac{u^{2} - 11 u + 30}{n^{4} - 7 n^{2} + 10}$

Factor $u^{2} - 11 u + 30$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $30$ and whose sum is $- 11$ .

$- 6, - 5$

Write the factored form using these integers.

$\frac{(u - 6) (u - 5)}{n^{4} - 7 n^{2} + 10}$

Replace all occurrences of $u$ with $n^{2}$ .

$\frac{(n^{2} - 6) (n^{2} - 5)}{n^{4} - 7 n^{2} + 10}$

Step 2

Simplify the denominator.

Rewrite $n^{4}$ as ${(n^{2})}^{2}$ .

$\frac{(n^{2} - 6) (n^{2} - 5)}{{(n^{2})}^{2} - 7 n^{2} + 10}$

Let $u = n^{2}$ . Substitute $u$ for all occurrences of $n^{2}$ .

$\frac{(n^{2} - 6) (n^{2} - 5)}{u^{2} - 7 u + 10}$

Factor $u^{2} - 7 u + 10$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $10$ and whose sum is $- 7$ .

$- 5, - 2$

Write the factored form using these integers.

$\frac{(n^{2} - 6) (n^{2} - 5)}{(u - 5) (u - 2)}$

Replace all occurrences of $u$ with $n^{2}$ .

$\frac{(n^{2} - 6) (n^{2} - 5)}{(n^{2} - 5) (n^{2} - 2)}$

Step 3

Cancel the common factor of $n^{2} - 5$ .

Cancel the common factor.

$\frac{(n^{2} - 6) (n^{2} - 5)}{(n^{2} - 5) (n^{2} - 2)}$

Rewrite the expression.

$\frac{n^{2} - 6}{n^{2} - 2}$

Simplify (n^4-11n^2+30)/(n^4-7n^2+10)

Related Questions

Support LCMGCF.com by disabling your adblocker.