Question

subtracting rational expressions:
7x x-2
--- - ------
2x 20x+16
please include steps if possible

Answer 1

\[\frac{7x}{2x} - \frac{x-2}{20x+16}\] ?

Answer 2

yes

Answer 3

just take Lcm 2x(20x+16) and solve in as usual way

Answer 4

\[\frac{7}{2} - \frac{x-2}{4(5x+4)}\]

Answer 5

multiply 2(5x+4) both top and bottom of fraction 7/2

Answer 6

Reduce the first fraction to 7/2. Now the common denominator is 2(10x+8) When you rewrite the first fraction with that denominator, it becomes 7(10x+8)/2(10x+8). since the second fraction already has that denominator, it does not change so now the problem is (70x+56-x+2)/2(10x+8) or (69x+58)/2(10x+8)

Answer 7

why 2(5x+4) and not 4(5x+4)?why 2(5x+4) and not 4(5x+4)?

Answer 8

why 2(5x+4) and not 4(5x+4)?

Answer 9

when i factor 20x+16 I get 4(5x+4)

Answer 10

why do you multiply times 2(5x+4) anmd not 4(5x+4)?

Answer 11

Because the first fraction has a denominator of two. So rewrite the denominator of the second fraction as 2(10x+8). Now ask yourself: By what should I multiply the first denominator which is 2 to get the second denominator which is 2(10x+8)? Isn't it clear that the answer is "multiply by (10x+8)"? Then do the same thing to the numerator.

Answer 12

how di you get 2(10x+8)?

Answer 13

did*

Answer 14

I took the denominator of the second fraction which is 20x + 16 and factored out a 2 . Since 20x+16 = 2(10x+8) they are equivalent

Answer 15

you're just trying to make it equal to the other denomitaor?

Answer 16

The reason I factored out the two is because the denominator of the first fraction is 2 and I wanted to see what I should multiply the first fraction by to get the same denominator the second fraction has.

Answer 17

or it always hast to be the lcm?

Answer 18

or it always hast to be the lcm?

Answer 19

Yes, love. You cannot subtract two fractions unless they have the same denominator.

Answer 20

but i mean you divide it to the lcm or just to make it equal to the other fraction?

Answer 21

It is most efficient if the denominator is the LCM of both denominators but not mandatory. If the denominators are the same then the fractions can be subtracted.

Answer 22

ok th

Answer 23

thanks

Answer 24

thanks

Answer 25

You can see that 20x+16 is the LCM of 2 and 20x+16. I only wrote 20x+16 as 2(10x+8) to make it clear that 20x+16 IS the LCM