How do you simplify #(x^2+2x-35)/ (x^2+4x-21) * (x^2+3x-18)/(x^2+9x+18)#?

Question

Nathan Axel · Accepted Answer

Simplify quadratic expression f(x)

Ans:# (x - 5)/(x + 3) # First factor all the trinomials: #(x^2 + 2x - 35) = (x - 5)(x + 7)#; # (x^2 + 3x - 18) = (x - 3)(x + 6)# #(x^2 + 4x - 21) = (x + 7)(x - 3)#; #(x^2 + 9x + 18) = (x + 3)(x + 6)# #f(x) = ((x - 5)(x + 7))/((x + 7)(x - 3)).((x - 3)(x +6))/((x + 3)(x + 6))#= #= (x - 5)/(x + 3)#

Avery Alexander · Answer

undefined To simplify the expression (x^2+2x-35)/(x^2+4x-21) * (x^2+3x-18)/(x^2+9x+18), we can factorize the numerator and denominator of each fraction and then cancel out any common factors.

The numerator of the first fraction, x^2+2x-35, can be factored as (x+7)(x-5). 
The denominator of the first fraction, x^2+4x-21, can be factored as (x+7)(x-3).

The numerator of the second fraction, x^2+3x-18, can be factored as (x+6)(x-3). 
The denominator of the second fraction, x^2+9x+18, can be factored as (x+6)(x+3).

Now, we can cancel out the common factors in the numerator and denominator of each fraction.

(x+7)(x-5)/(x+7)(x-3) * (x+6)(x-3)/(x+6)(x+3)

After canceling out the common factors, we are left with:

(x-5)/(x-3) * 1/(x+3)

Simplifying further, we can multiply the numerators and denominators:

(x-5)/(x-3) * 1/(x+3) = (x-5)/(x-3)(x+3)

Therefore, the simplified expression is (x-5)/(x-3)(x+3).