Help me with these Solving Rational Equations math problems please?? Im so lost?

Question

HOW do you solve this??? they're in fraction form

Y/10 = 2/5 + 3/8 the answer in the book is 31/4


1/4 - 5/6= 1/9 the answer in the book is 12/7


3/8 + 1/3= 1/12 The book has no answer to help solve this?


5/8 - 2/5= 1/Y No answer for this one also..? =[

How did they come up with the answers above. My book doesnt show any work just the answer! ANY HELP PLEASE???

the variables in the last few problems I typed are missing because that's how they are in the book.

Answer 1

What you have to do is make all of the fractions have a common denomenator, meaning, the same number at the bottom.

You can do this by multiplying the top number and bottom number in a fraction to get a higher number.

For example, the first one...

Your denomenators are 10, 5, and 8. The lowest common multiple of those three numbers (the lowest whole number that those can all go into easily) is 40. I did that by multiplying 8 by 5, and then it happened to also work for 10.

So, you then multiply Y by 4 (like you do the 10 to get 40), and the 2 by 8 (like you do the 5 to get 40) and the 3 by 5 (like you do the 8 to get 40). Since now all of your fractions have the denomenator of 40, the laws of algebra say that you can ignore the fraction, and just have 4*Y=16+15.... Solve for Y, and you get 31/4.

That method will work for all of those. Good luck.

Answer 2

I'm not really clear on what you are looking for here... but here goes:

Y/10 = 2/5 + 3/8
I'll solve for y
multiply through by 10
y = (2*10) / 5 + (3*10) / 8
=20/5 + 30/8

lowest common denominator is 40, so multiply as follows:
y = 20/5 * 8/8 + 30/8* 5/5
= 160/40 + 150 / 40
=310/40 = 31/4


For 1/4 - 5/6, consider the lowest common denominator is 12, so

1/4 - 5/6 = 1/4 * 3/3 - 5/6*2/2
=3/12 - 10/12 = -7/12 .... I think something is mssing in your question.


3/8 + 1/3 has the lowest common deniominator 24 so
3/8 + 1/3 = 3/8 * 3/3 +1/3* 8/8
= 3/24+ 8/24 = 11/24 Again, there is no"y" to solve for in your equation???


5/8 - 2/5= 1/Y
Multiply through by "y"
1 = 5/8y - 2/5y
again, lowest common denominator is 40 so
1 = (5/8)*(5/5)*y - (2/5)*(8/8)*y
1 = 25/40 y - 16/40 y
1 = 9/40 y
and
y = 1* 40/9 = 40/9 = 4 and 4/9

Answer 3

Y/10 = 2/5 + 3/8
= (2×8 + 3×5) / (5×8)
= 31/40
So Y = 10 × 31/40 = 31/4.

The variable seems to be missing in the next two equations. I can't work out what they were supposed to be.

5/8 - 2/5 = 1/Y: LCD on left is 40
<=> (5×5 - 2×8) / 40 = 1/Y
<=> 9/40 = 1/Y
<=> Y = 40/9.

Answer 4

First put you're variables on one side, and regular number on the other (in fracton from)

Y/10 = 2/5 + 3/8 (this one was already set up)

next find a least common deminator for the right hand side. In this case, it is 40 becasue both 5 and 8 are factors of 40

Y/10 = (2*8)/40 + (3*5)/40

Work out the right hand side to one number

Y/10 = 16/40 + 15/40
Y/10 = (16+15)/40
Y/10 = 31/40

Finally, to get the variable "y" by itself, multiply both sides by 10

(10*Y)/10 = (10*31)/40

Cancle out you're 10's on the left hand side, and reduce the right hand side

Y= 310/40
Y=31/4

That's it. You left out the variables on the next three problems, so I can't help you.



Fourth Problem:

Same beginning setup. Find Least common deminator and add the number together.

(5*5)/40 - (2*8)/40 = 1/Y
(25-16)/40 = 1/Y
9/40 = 1/Y

Now, to get "y" on the left hand side, multiply both sides by Y
y*(9/40) = 1
(9Y)/40 = 1

Now multiply both sides by 40 and divide by 9 to get "y" by itself

Y = 40/9

Hope this helps!

Answer 5

a million. worry-unfastened denominator on left hand area of the equation: [x-a million - (x+3)] / (x-a million)(x+3) (x-a million-x-3) / (x^2 + 2x - 3) -4 / (x^2 + 2x - 3) 2. Now the equation is: -4 / (x^2 + 2x - 3) = (x+a million) / (x^2 + 2x - 3) The denominators are the comparable, as a results of fact of this we require: -4 = x+a million -4 = x+a million x = -5

Answer 6

Are you clear about LCM (Lowest Common Multiple) of two or more numbers ? That's the key.