Question

help me?(:

Answer 1

Simplify completely quantity 8 x minus 16 over quantity x squared minus 13 x plus 22 and find the restrictions on the variable.

Answer 2

for the nominator i got 8(x-2) but idk how to do the denominator..

Answer 3

Ok you got the numerator right.

Answer 4

Now the denominator is a quadratic. You have to solve it to get two possible solutions for the denominator, and the equation as well.

Answer 5

Consider the denominator now:\[x ^{2}-13x-22\]
\[x ^{2}-11x-2x+22\]
Taking the common factors in this simplified denominator, we get:
\[x(x-11)-2(x-11)\]
Hence the denominator can no be written as
\[(x-2)(x-11)\]
The factor \[x-2\] appears both in the num and d denominator, so cancel it out, and you will get the final simplified equation.

Answer 6

wait how did you get 2x+22?

Answer 7

The denominator is \[x ^{2}-13x+22\] right?

Answer 8

yes

Answer 9

Alright, now here is what you do to solve a quadratic like that: You split the middle term (in this case 13x) into two factors the sum of which is equal to the middle term, and the product of which is equal to the last term (22 in this case). Can you think of such two numbers? Yes, they are -11 and -2. Hence we get 2x+22.

Answer 10

oh, sorry i totally forgot about that. slow moment. 8 over quantity x minus 11, x ≠ 2, x ≠ 11, is that the answer though?

Answer 11

Absolutely correct! :-)