can you solve and give me the formula?

Question

Can you solve and give me the formula?
the directions go as follows:
perform the following operations and then simplify.
(2x² + 3x - x² + 3x + 21 - x - 7) / (x² - 2x - 63)

that is 2x squared + 3x - x squared + 3x + 21 - x-7
over
x squared - 2x - 63

the problem is, x equals x. The answer is (x-2)/(x-9), that is the answer in the back of the book, but I want to know how they got that answer. thank you

wow shreef that was a great answer. I should have thought of that

Answer 1

ok what ya got here after the adding in the numerator is:

x^2+5x+14
_________
x^2-2x-63


let's factor each term

(x+7)(x-2)
________
(x+7)(x-9)


(x+7) cancels out and you're left with (x-2)/(x-9)

on a personal note i'd like to say that factoring is demon spawn

Answer 2

well first you have to collect like terms
(2x squared - x squared +3x + 3x - x + 21 - 7) / (x squared -2x -63
= ( x squared + 6x -x +14 ) / ( x squared -2x -63 )
= ( x squared + 5x+ 14 ) / (x squared -2x - 63 )
now that you collected all the like terms you can foil both equation.
= ( x + 7 ) ( x + 2 ) / ( x-9 ) ( x+7 )
=since the both have ( x + 7 ) on the bottom and top then you can cross it out ( simplify )
= ( x + 2 ) / ( x - 9 ) or ( x -2 ) / ( x + 9 ) ...
i think you might have made a typo cause unless the its ( 2x squared + 3x - x squared + 3x - 21 + 7 ).... then the answer would turn up to be
( x - 2 ) / ( x + 9) or else the equation can not be solved

Answer 3

(2x² + 3x - x² + 3x + 21 - x - 7) / (x² - 2x - 63)

The first thing to do is to collect like terms. I'll rearrange the terms first so you can see what's being combined:

(2x² - x² + 3x + 3x - x + 21 - 7) / (x² - 2x - 63)

Now put the terms together:

(x² + 5x + 14) / (x² - 2x - 63)

Now, at this point, I begin to suspect that there is a typo in either your book or the version of the problem you posted -- if the problem reduced to (x²+5x-14)/(x²-2x-63), it would easily factor as (x+7)(x-2)/((x+7)(x-9)), the x+7 would cancel, and the result would indeed be (x-2)/(x-9). However, they instead put +14, and as a result the polynomial on top is irreducible over the reals. As such, no factors can cancel, and (x² + 5x + 14) / (x² - 2x - 63) is the simplest form.

Answer 4

My computer won't handle powers well so
x squared = x^2 OK?

2x^2 + 3x - x^2 + 3x + 21 - x - 7
= x^2 + 5x -14
= (x + 7)(x-2) that is on top

On the bottom: x^2 - 2x - 63 = (x - 9)(x + 7)

The factor (x + 7) is on the top and bottom and so it cancels out which leaves you with:
(x -2) over (x - 9) tadaaaaa

Answer 5

Combine like terms and factor (2x^2-x^2)+(3x+3x-x)+21-7=
x^2 + 5x + 14 /
x^2-2x-63= (x-9)(x+7)

Either you copied question wrong or book is wrong.
Also I noticed that other answers somehow got (21-7=-14)that must be advanced math.

Answer 6

2x^2+3x-x^2+3x-21-x+7/
x^2-2x-63
Combine like terms in the numerator:
x^2+5x-14/x^2-2x-63=
(x-2)(x+7)/(x+7)(x-9)
Cancel out the x+7:
(x-2)/(x-9)

Answer 7

You have a typo. Probably its -21 and +7 in the numerator.

Answer 8

A=a million/2bh start up via multiplying a million/2's reciprocal (opposite=2, turn the numbers) then divide each little thing via 2: 2A=bh (the a million/2 is canceled) to discover b divide each little thing via h and you get: 2A/h=b

Answer 9

A compliment to Leo_07's answer: x cannot be -7.

Answer 10

Ok.
EDIT
Hahaha I was wrong. I completely forgot about factoring!!! Ha sorry. I was never really good at that...