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

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1. moneybird Group Title

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

2. neverforgetvivistee Group Title

yes

3. PratikBhandari Group Title

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

4. moneybird Group Title

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

5. moneybird Group Title

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

6. Mertsj Group Title

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 Group Title

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

8. neverforgetvivistee Group Title

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

9. neverforgetvivistee Group Title

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

10. neverforgetvivistee Group Title

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

11. Mertsj Group Title

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 Group Title

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

13. neverforgetvivistee Group Title

did*

14. Mertsj Group Title

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 Group Title

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

16. Mertsj Group Title

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 Group Title

or it always hast to be the lcm?

18. neverforgetvivistee Group Title

or it always hast to be the lcm?

19. Mertsj Group Title

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

20. neverforgetvivistee Group Title

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

21. Mertsj Group Title

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 Group Title

ok th

23. neverforgetvivistee Group Title

thanks

24. neverforgetvivistee Group Title

thanks

25. Mertsj Group Title

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