Question

What is the solution to the rational equation (3)/(2)-(1)/(x-5)=(-2)/(2x-10)? Can someone please help me!

Answer 1

You can cross multiply to get your answer. Don't forget to check the answers you get to make sure that your answers work and aren't extraneous (A solution of a simplified version of an equation that does not satisfy the original equation.) http://www.mathwords.com/e/extraneous_solution.htm

Answer 2

okay @wonder291

Answer 3

but what exactly do i do to the other side of the equation

Answer 4

\[\frac{ 3 }{ 2 }-\frac{ 1 }{ x-5 }=\frac{ -2 }{ 2x-10 }\]
You could multiple the entire equation by the least common multiple of all the denominators...

Then you could combine like terms

Answer 5

could you guide me through the problem im struggling on this a lot.

Answer 6

The Least Common Multiple (LCM) is basically the smallest (non-zero) number that is a multiple of two or more numbers. http://www.mathsisfun.com/least-common-multiple.html

The same works for expressions with variables.

For example, in this problem the numbers we have (to find the LCM of) are
2, x-5, and 2x-10.

Answer 7

okayy

Answer 8

Do you still need help with anything?

Answer 9

Yes i am really trying my hardest to solve this problem but i just get confused on it .

Answer 10

What step are you on now?

Answer 11

cross multiplying

Answer 12

Let me show you an example with other numbers

\[\frac{ 2 }{ 3 }=\frac{ 4 }{ 6 }\]
Cross multiplying in this example means you multiple one numerator by the other denominator.

2*6=3*4
12=12

The same would work with these expressions with variables.

Answer 13

this is what i got 3x-15-1=(-2)/(2x-10)

Answer 14

\[\frac{ 3 }{ 2 }-\frac{ 1 }{ x-5 }=\frac{ -2 }{ 2x-10 }\]
What did you get for the least common multiple?

Answer 15

i Really dont know :(

Answer 16

It's ok, I'll help you...

To find the least common multiple (denominator because they're a fraction) for the following,
2, x-5, and 2x-10.
Try multiplying factors together so that you only have 1 factor. Try not to multiply all of them at once; try two at a time.

Answer 17

okay i did it but it did not work

Answer 18

another way to find it is to see if some factors divide into other factors

Answer 19

for example, for 5, 2x+1, 10x+5
10x+5 is divisible by 5; and it is divisible by 2x+1; therefore it is the least common multiple

Answer 20

It will work for 2, x-5, and 2x-10.

Answer 21

for the example, 10x+5 is the least common multiple

Answer 22

okay i multiplied them all by the lcm what do i do next

Answer 23

You can combine like terms. for example:
2x+1+5x
2x and 5x are like terms.
so you end up with
7x+1

Answer 24

but before that, make sure you multiply everything out

Answer 25

okay is the answer X=5

Answer 26

substitute the answer you get back into the equation (to check), and remember that the denominator can never equal 0!

Answer 27

i Believe this is right x=5

Answer 28

If none of your solutions work, then there is no solution to the equation! (sometimes this happens)

Answer 29

Oh so its no solution because it was'nt quite working

Answer 30

\[\frac{ 3 }{ 2 }-\frac{ 1 }{ x-5 }=\frac{ -2 }{ 2x-10 }\]

Yes, just for this rational equation.

Answer 31

thankyou soo much for the guidance

Answer 32

No problem! :)