## neverforgetvivistee 4 years ago subtracting rational expressions: 7x x-2 --- - ------ 2x 20x+16 please include steps if possible

1. moneybird

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

2. neverforgetvivistee

yes

3. PratikBhandari

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

4. moneybird

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

5. moneybird

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

6. Mertsj

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)

7. neverforgetvivistee

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

8. neverforgetvivistee

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

9. neverforgetvivistee

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

10. neverforgetvivistee

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

11. Mertsj

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.

12. neverforgetvivistee

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

13. neverforgetvivistee

did*

14. Mertsj

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

15. neverforgetvivistee

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

16. Mertsj

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.

17. neverforgetvivistee

or it always hast to be the lcm?

18. neverforgetvivistee

or it always hast to be the lcm?

19. Mertsj

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

20. neverforgetvivistee

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

21. Mertsj

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.

22. neverforgetvivistee

ok th

23. neverforgetvivistee

thanks

24. neverforgetvivistee

thanks

25. Mertsj

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