(x-5)(2+7x) over (5-x)(7x+2)
please explain how to do this
2007-01-03 11:38:04 · 10 answers · asked by alyssa p 1 in Education & Reference ➔ Homework Help
This problem demonstrates several properties of algebra, including the commutative property of addition, which simply states that the order in which the numbers appear in an addition problem does not change the value of the sum. For example, 1 + 2 is equal to 2 + 1, as they both give the sum of 3.
For this problem, either the first term of (2+7x) or the second term of (7x+2) can be rearranged to mirror the identical term. In this case, I will demonstrate rearranging the first term. By doing so, we arrive at:
[(x-5)(7x+2)] / [(5-x)(7x+2)]
Note: Brackets are used to denote the entire numerator from the denominator.
At this point, we can eliminate both (7x+2) terms from the both numerator and denominator. The explanation behind this lies in the fact that identical terms cancel each other out. For example, 2/2 and 3/3 each equal 1. For this reason, (7x+2)/(7x+2) is also equal to 1. Now we are left with:
(x-5) / (5-x)
Next, we can pull out a -1 from the denominator in order to create a duplicate term in the denominator. This is done in order to mimic the previous step and eliminate like terms. We now have:
(x-5) / -(x-5)
At this point, we cross out the like terms, leaving us with 1 / -1. This fraction later simplifies, leaving the answer at -1.
2007-01-03 11:56:42 · answer #1 · answered by Jon 1 · 0⤊ 0⤋
If you've written the question correctly, it's actually rather simple and you don't need to bother with FOIL. The second set of parentheses in your numerator is 2+7x, as is the second set of parentheses in your denominator. They cancel each other out and you are left with:
x-5
-----
5-x
Now, let's factor a - out of the denominator. You are left with:
x-5
-----
-(x-5)
Your answer is -1.
ADDED: The Annoying Thing ALMOST had the FOIL approach to it correct. Unfortunately, when he switched the signs in the denominator, he forgot to leave a - outside the brackets. You can't just switch signs for the heck of it. -5+4 isn't the same thing as 5-4!
2007-01-03 11:46:13 · answer #2 · answered by glurpy 7 · 2⤊ 0⤋
when you divide a number by a fraction it is equivalent to multiplying by the reciprocal of that fraction, so when you divide a fraction by 1/2, it is really like multiplying it by 2. so you would just really find half of 3/11 which is 3/22. FYI, doubling 3/11 would give 6/11 not 6/22. 6/22 is just another way to write 3/11 (6/22 would reduce to 3/11, since as your daughter put it "you can't put even numbers over even numbers"...they can be reduced to lower terms if you did).
2016-05-23 00:07:27 · answer #3 · answered by ? 4 · 0⤊ 0⤋
at this point in math (algebra i'm guessing) you want to learn quick ''shortcuts''
(2+7x) and (7x+2) if you can see are the same by the communitive property so they cancel to 1
(x-5) and (5-x)... any time you see something like this (only is both are subtraction inside) they will cancel to -1
so 1 times -1= -1
2007-01-03 11:44:38 · answer #4 · answered by Zaza 5 · 1⤊ 0⤋
The FOIL rule is a mnemonic for remembering how to multiply two binomials (polynomials with two terms). The name comes from the order of multiplying terms of the binomials:
First ("first" terms of each binomial are multiplied together)
Outer ("outer" terms multiplied)
Inner ("inner" terms multiplied)
Last ("last" terms multiplied)
So multiply x*2, x*7x, -5*2, and -5*7x. Do the same with the other part, then divide.
Should I continue explaining? I can walk you through the whole thing :D I'd just hate to do it for you!
2007-01-03 11:40:19 · answer #5 · answered by mizz_milk06 4 · 0⤊ 1⤋
(x - 5) (2 + 7x) / (5 - x) (7x + 2)
2x + 7x^2 - 10 - 35x / 35x + 10 - 7x^2 - 2x
7x^2 - 33x - 10 / (-7x^2 + 33x + 10) : switch signs of this inequality
7x^2 - 33x - 10 / 7x^2 - 33x - 10... both cancel out each other...
Answer: 1
2007-01-03 11:46:02 · answer #6 · answered by The Annoying Thing 2 · 0⤊ 2⤋
well the answer is negative one. This is because the numerator and denomerator are the same value, but one is negative and the other is positive.
2007-01-03 12:07:51 · answer #7 · answered by Jonny 1 · 0⤊ 0⤋
foil..
7x^2+2x-35x-10
-------------------- = 1,
-7x^2 +35x - 2x+10
they all cancel each other out
4 negatives=positive
2007-01-03 11:43:47 · answer #8 · answered by daddy's_girl 2 · 0⤊ 2⤋
From what know i think the answer is -10x-35x/-35x-10x which equals -46x/-46x which means they cancel out,giving you 1
I think one is the answer.
2007-01-03 11:53:28 · answer #9 · answered by reba 1 · 0⤊ 1⤋
r u solving for x??
2007-01-03 11:40:22 · answer #10 · answered by Carroll Patriot 2 · 0⤊ 1⤋