Question

simplify completely x^2 - 3x - 54 / x^2 - 18x +81 (multiply) x^2 + 12x + 36 / x + 6

Answer 1

Its weird because I get the ones with vairables, but these which most of the time would seem easier, just doesnt click and for me seems to take 10 times more time/ effort then the ones with variables.

Answer 2

\[\Large \frac{x^{2}-3x-54}{x^{2}-18x+81}*\frac{x^{2}+12x+36}{x+6}\]

Step 1. Factor the first numerator.
Step 2. Factor the first denominator.
Step 3. Factor the second numerator.

Keep in mind:
\[\Large x^{2}+(a+b)x+(a*b)\]

In otherwords, what two numbers when added together get you the middle number, and when multiplied get you the last one?

Example:
Step 1:
6+-9=-3
6*(-9) = -54
Therefore step 1 = (x+6)(x-9)

Answer 3

(x2 -3x -54) / (x2 -18x + 81) * (x2 +12x +36) / (x+6)

x2 -3x -54 = x2 -9x +6x -54 = x(x-9) +6 (x-9) = (x - 9) (x +6)
x2 -18x + 81= x2 -9x -9x + 81 = (x - 9) (x -9)
x2 +12x +36 = x2 +6x +6x +36 = (x +6) ( x +6)

Now substituteall this values in equation..