How do you simplify #(2x+4 )/( x^2+11x+18) div( x+1) /( x^2+14x+45)#?

Question

Nathan Axel · Accepted Answer

The simplified version of that expression is #2(x+5)/(x+1)# I factorized and changed the division into a product (inverting the second fraction) to get: #(2(x+2))/((x+2)(x+9))xx((x+5)(x+9))/(x+1)=# #=(2cancel((x+2)))/(cancel((x+2))cancel((x+9)))xx((x+5)cancel((x+9)))/(x+1)=# #=2(x+5)/(x+1)#

Eli Assouline · Answer

undefined To simplify the expression (2x+4)/(x^2+11x+18) ÷ (x+1)/(x^2+14x+45), we can multiply the first fraction by the reciprocal of the second fraction.

Reciprocal of (x+1)/(x^2+14x+45) is (x^2+14x+45)/(x+1).

So, the expression simplifies to (2x+4)/(x^2+11x+18) * (x^2+14x+45)/(x+1).

Now, we can simplify further by canceling out common factors between the numerator and denominator.

The numerator (2x+4) does not have any common factors with the denominator (x^2+11x+18).

The numerator (x^2+14x+45) has common factors of (x+5) and (x+9) with the denominator (x+1).

After canceling out the common factors, the expression simplifies to:

(2x+4)/(x^2+11x+18) * (x^2+14x+45)/(x+1) = (2x+4)/(x^2+11x+18) * [(x+5)(x+9)]/(x+1).

This is the simplified form of the given expression.