anonymous
  • anonymous
Will you help me figure out the solution to this rational equation? (x/2x - 1) + 1/4 = 2/2x - 1
Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
\[\frac{ x }{ 2x-1 }+\frac{ 1 }{ 4 }=\frac{ 2 }{ 2x-1 }\]
anonymous
  • anonymous
Answer Choices A. x = \[\frac{ 9 }{ 2 }\]B. x = \[\frac{ 7 }{ 2 }\] C. x = \[\frac{ 3 }{ 2 }\] D. x = \[\frac{ 7 }{ 6 }\]
anonymous
  • anonymous
@tom982 Any ideas?

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anonymous
  • anonymous
I know I have to have a common denominator...
anonymous
  • anonymous
help anyone!?
anonymous
  • anonymous
Hi sorry, I left this tab open. Firstly, thanks for taking the time to draw out this equation using the editor, it's so much easier to read and it's nice to see people making an effort. Looking at our fractions, we can't merge them as the denominators aren't the same but there are other things we can do, like multiplying through by (2x-1) giving: \[\frac{ x(2x-1) }{ 2x-1 }+\frac{ (2x-1) }{ 4 }=\frac{ 2(2x-1) }{ 2x-1 }\]We're able to do this as we've done the same to both sides. Now we can cancel out some of the terms to get:\[x+\frac{ (2x-1) }{ 4 }=2\]Now we can times everything by 4 to get rid of that last fraction:\[4x+\frac{ 4(2x-1) }{ 4 }=4\times2\]Giving\[4x+(2x-1)=8\]Can you do the last few steps to find x?
anonymous
  • anonymous
1. Add 1 to both sides, canceling out the 1 on the left side of the equal sign. I'm left with \[4x + 2x = 9\]. 2. Combine like terms, so I'm left with 6x = 9. 3. Divide 6 from both sides, so I end up with 9/6, which simplifies to 3/2. The answer is C. x = 3/2. Is this correct @tom982 ?
anonymous
  • anonymous
Fantastic explanation by the way. I appreciate it so much!
anonymous
  • anonymous
Spot on, excellent work. You can check this answer by substituting x=3/2 into your original equation and seeing that both sides are equal. Glad you liked the explanation, I was a bit unsure which way to show you but looks like I picked a good one. Here's another way to do it just for future reference: \[\frac{ x }{ 2x-1 }+\frac{ 1 }{ 4 }=\frac{ 2 }{ 2x-1 }\]\[\frac{ 4x }{ 4(2x-1) }+\frac{ (2x-1) }{ 4(2x-1) }=\frac{ 8 }{ 4(2x-1) }\]Now we have the same denominator for all 3, multiplying through by 4(2x-1) only leaves the numerators as an equation: 4x+(2x-1)=8 which you solved perfectly before.
anonymous
  • anonymous
Wow. I appreciate your time and effort. Gracias por ayudarme! Thank you for helping me! @tom982

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