SOLUTION: Solve (finding a least common denominators). x-7/x+2 = 1/4 Thanks in advance for anyone who can help!! :) I can't find a least common denominator.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve (finding a least common denominators). x-7/x+2 = 1/4 Thanks in advance for anyone who can help!! :) I can't find a least common denominator.       Log On


   

Question 189707This question is from textbook Prentice Hall Algebra 1
: Solve (finding a least common denominators).
x-7/x+2 = 1/4
Thanks in advance for anyone who can help!! :) I can't find a least common denominator.
This question is from textbook Prentice Hall Algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Is the equation %28x-7%29%2F%28x%2B2%29+=+1%2F4+ ???


%28x-7%29%2F%28x%2B2%29+=+1%2F4+ Start with the given equation.


4%28x-7%29+=+1%28x%2B2%29 Cross multiply


4x-28=x%2B2 Distribute.


4x=x%2B2%2B28 Add 28 to both sides.


4x-x=2%2B28 Subtract x from both sides.


3x=2%2B28 Combine like terms on the left side.


3x=30 Combine like terms on the right side.


x=%2830%29%2F%283%29 Divide both sides by 3 to isolate x.


x=10 Reduce.


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Answer:

So the answer is x=10







OR...

Is the equation x-7%2F%28x%2B2%29+=+1%2F4 ????



x-7%2F%28x%2B2%29+=+1%2F4 Start with the given equation.


Multiply EVERY term by the LCD 4%28x%2B2%29 to clear the fractions.


4x%28x%2B2%29-4%287%29=x%2B2 Simplify


4x%28x%2B2%29-28=x%2B2 Multiply


4x%5E2%2B8x-28=x%2B2 Distribute


4x%5E2%2B8x-28-x-2=0 Get everything to the left side


4x%5E2%2B7x-30=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=4, b=7, and c=-30


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%287%29+%2B-+sqrt%28+%287%29%5E2-4%284%29%28-30%29+%29%29%2F%282%284%29%29 Plug in a=4, b=7, and c=-30


x+=+%28-7+%2B-+sqrt%28+49-4%284%29%28-30%29+%29%29%2F%282%284%29%29 Square 7 to get 49.


x+=+%28-7+%2B-+sqrt%28+49--480+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-30%29 to get -480


x+=+%28-7+%2B-+sqrt%28+49%2B480+%29%29%2F%282%284%29%29 Rewrite sqrt%2849--480%29 as sqrt%2849%2B480%29


x+=+%28-7+%2B-+sqrt%28+529+%29%29%2F%282%284%29%29 Add 49 to 480 to get 529


x+=+%28-7+%2B-+sqrt%28+529+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%28-7+%2B-+23%29%2F%288%29 Take the square root of 529 to get 23.


x+=+%28-7+%2B+23%29%2F%288%29 or x+=+%28-7+-+23%29%2F%288%29 Break up the expression.


x+=+%2816%29%2F%288%29 or x+=++%28-30%29%2F%288%29 Combine like terms.


x+=+2 or x+=+-15%2F4 Simplify.


So the answers are x+=+2 or x+=+-15%2F4






OR...

Is the equation %28x-7%29%2Fx%2B2+=+1%2F4 ????


%28x-7%29%2Fx%2B2+=+1%2F4 Start with the given equation.


4%2Across%28x%29%28%28x-7%29%2Fcross%28x%29%29%2B8x+=+cross%284%29x%281%2Fcross%284%29%29 Multiply EVERY term by the LCD 4x to clear the fractions.


4%28x-7%29%2B8x=x Simplify


4x-28%2B8x=x Distribute.


12x-28=x Combine like terms on the left side.


12x=x%2B28 Add 28 to both sides.


12x-x=28 Subtract x from both sides.


11x=28 Combine like terms on the left side.


x=%2828%29%2F%2811%29 Divide both sides by 11 to isolate x.


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Answer:

So the answer is x=28%2F11 which approximates to .