9z-42z-72/3z^2+28z+32divided by 2z^2+10z-48/z^2-9z+18
Can someone help me? I know they're supposed to be flipped and factored, and I did that, but afterwards I can only get as far as:
9z+12/3z+4*2z-6/z-3
Wait, I wrote it wrong. This is the correct way:
(9z-42z-72)/(3z^2+28z+32)divided by(z^2-9z+18)/(2z^2+10z-48)
my factors were
[(3z+4)(3z-18)]/[3z+4)(z+8)] x [(2z-6)(z+8)]/[(z-3)(z-6)]
= 6 , z not equal to -4/3, -8, 3, or 6
I don't understand. If you do it that way, your z-3 doesn't cancel and then i don't know where to go from there.
notice at the top there was a 2z-6
which is 2(z-3)
there is also 3z-18 at the top which
is 3(z-6)
so the z-3 and the z-6 at the bottom cancel with the rest of the stuff leaving only the 3x2 at the top
Thank you for answering, but I'm so confused. Can someone else help, please?
To simplify the expression (9z - 42z - 72) / (3z^2 + 28z + 32) divided by (2z^2 + 10z - 48) / (z^2 - 9z + 18), you correctly identified that you need to flip the second fraction and then factor both the numerator and denominator of each fraction. Let's go through the steps:
Step 1: Factor the numerator and denominator of the first fraction:
The numerator, 9z - 42z - 72, can be combined as -33z - 72.
The denominator, 3z^2 + 28z + 32, can be factored as (3z + 8)(z + 4).
Therefore, the first fraction simplifies to: -33z - 72 / (3z + 8)(z + 4).
Step 2: Factor the numerator and denominator of the second fraction:
The numerator, 2z^2 + 10z - 48, can be factored as 2(z + 8)(z - 3).
The denominator, z^2 - 9z + 18, can be factored as (z - 3)(z - 6).
Therefore, the second fraction simplifies to: 2(z + 8)(z - 3) / (z - 3)(z - 6).
Step 3: Flip the second fraction and multiply:
Multiplying the first fraction by the reciprocal of the second fraction gives:
-33z - 72 / (3z + 8)(z + 4) * (z - 3)(z - 6) / 2(z + 8)(z - 3).
Step 4: Simplify by canceling out common factors:
The (z - 3) factor in the numerator of the first fraction cancels out with the (z - 3) factor in the denominator of the second fraction.
The expression can be further simplified as:
-33z - 72 / (3z + 8)(z + 4) * (z - 6) / 2(z + 8).
And that's the simplified expression after factoring and canceling out common factors.