Rational Equations?

Question

Would you please explain the answer of this problem to me.

(5x/ 3x +1) - (1/9x + 3) = (7/6)

Thanks

Answer 1

Assuming that equation is:-
(5x) / (3x + 1) - 1 / [ (3) (3x + 1) ] = 7 / 6
15x - 1 = 21 (3x + 1) / 6
90x - 6 = 21(3x + 1)
90x - 6 = 63x + 21
27x = 27
x = 1

Answer 2

You need to rewrite the equation so that all the X's are together, and simplify things. I'm not entirely sure what things go on top and what on bottom with how you wrote it. If you meant the first part to be (5x)/(3x) , then there's an X on the top and bottom, so they cancel out and you get 5/3, so the first part would become (5/3)-1 = (5/3)-(3/3) = (5-3)/3 = 2/3.

If you meant the first part to be (5x)/(3x+1) and the second as (1)/(9x+3), you will have to find the lowest common denominator - notice that in the second denominator both 9 and 3 are divisible by 3, so you can rewrite the second term (1)/(3*(3x+1)). So you should rewrite the first term similarly by putting a 3 on the top and the bottom:

(3*5x)/(3*(3x+1))+(1)/(3*(3x+1)) =
(15x+1)/(3*(3x+1)) = 7/6
cross multiply
(15x+1)*6 = (3*(3x+1))*7

You can now multiply out everything, and get all the X's on the same side to solve.

Answer 3

5x / (3x + 1) - 1 / (9x + 3) = 7/6

5x / (3x + 1) - 1/[3(3x + 1)] = 7/6 //multiply by 3(3x + 1)

5x * 3 - 1 = 7(3x + 1)/2 // multiply by 2

6*5x - 2 = 7(3x + 1)

30x - 2 = 21x + 7 // - 21x

9x - 2 = 7 // + 2

9x = 9 // divide by 9

x=1

Checking the solution:
5/(3 + 1) - 1/(9 + 3) =? 7/6

5/4 - 1/12 =? 7/6

15/12 - 1/12 =? 7/6

14/12 =? 7/6

Well, 14/12 can be reduced to 7/6. The answer is yes.

Answer 4

(5x/ 3x +1) - (1/9x + 3) = (7/6)

5x / (3x+1) - 1/(3*(3x+1)) =7/6

5x - 1/3 = 7*(3x+1)/6

30X -2 = 21x +7

9x = 9

x = 1

Answer 5

5x/(3x+1) - 1/(9x+3) = 7/6
multiply through by 6(3x+1)
30x-2=21x+7
9x=9
x=1

Answer 6

multiply out the brackets first
so it is now

5x/3x+1-1/9x-3=7/6

then do all da x value and then the numarical value

simple: 5x/3x-1/9x and 1-3

so it is now: 1x(5/3-1/9)-3=7/6
the inverse of it is (5/3-1/9)/1x-3=6/7

and now find the answer it is easy now

Answer 7

(5x/(3x+1) - (1/(9x+3) = 7/6
(15x-1)/(9x+3)=7/6
6(15x-1)=7(9x+3)
90x-6=63x+21
90x-63x=21+6
27x=27
x=27/27=1

Answer 8

it will be:
(5x/3x+3x/3x)-(1/9x+27x/9x)

then

8x/3x - ((1+27x)/9x)

which means

24x/9x - ((1+27x)/9x)

and

(-1-3x)/9x

so

-1/9x - 3x/9x

ummmm

-1/9x - 1/3 = 7/6

well

-1/9x = 9/6

finaly

9x = - 6/9

x = - 2/27

i wish its right..

Answer 9

... 10/(x-a million) + a million = 20/(x²-a million) ... x ? ±a million ? Else equation turns into undefined or 10/(x-a million) + a million = 20/[ (x-a million)(x+a million) ] or 10(x+a million) + (x-a million)(x+a million) = 20 or 10x + 10 + x² - a million = 20 or x² + 10x - 11 = 0 or (x - a million) (x + 11) = 0 or x = a million ....... ? Reject via preliminary constraint or x = -11 .... ? very final answer

Answer 10

First off, remember to always use your parentheses clearly, help us help you!

E.g. Did you mean (5x/3x)+1 or (5x/(3x+1))? I'll assume you meant that second case.

The answer is x=1.