SOLUTION: I need to prove that ((x+4)/(3x^2-7x))=(((1/x)+(4/x^2))/(3-(7/x))) By showing the steps, So far I have tried working from the right side of the equation to get to the left

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need to prove that ((x+4)/(3x^2-7x))=(((1/x)+(4/x^2))/(3-(7/x))) By showing the steps, So far I have tried working from the right side of the equation to get to the left      Log On


   

Question 775978: I need to prove that
((x+4)/(3x^2-7x))=(((1/x)+(4/x^2))/(3-(7/x)))
By showing the steps,
So far I have tried working from the right side of the equation to get to the left, and made it into a complex fraction and combined it, then multiplied the numerator by the denominators reciprocal in order to make it a normal fraction and ended up with ((1-x)(1-4)/(3-7)(x^2-x))
Found 3 solutions by MathLover1, tanjo3, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
Answer by tanjo3(60) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B4%29%2F%283+x%5E2-7+x%29+=+%281%2Fx%2B4%2Fx%5E2%29%2F%283-7%2Fx%29

Let's leave the left side as is and only deal with the right side:
%281%2Fx%2B4%2Fx%5E2%29%2F%283-7%2Fx%29

For the numerator and denominator, find a common denominator:
%28x%2Fx%5E2%2B4%2Fx%5E2%29%2F%283+x%2Fx-7%2Fx%29

We can rewrite it as:
%28%28x%2B4%29%2Fx%5E2%29%2F%28%283x-7%29%2Fx%29

Division with fraction means taking the reciprocal of the second number and multiplying.
%28%28x%2B4%29%2Fx%5E2%29%28x%2F%283x-7%29%29

Simplify.
%28x%2B4%29%2F%28x%283x-7%29%29
%28x%2B4%29%2F%283+x%5E2-7+x%29%29

Now we can see that the right side is equal to the left side.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

I need to prove that
((x+4)/(3x^2-7x))=(((1/x)+(4/x^2))/(3-(7/x)))
By showing the steps,
So far I have tried working from the right side of the equation to get to the left, and made it into a complex fraction and combined it, then multiplied the numerator by the denominators reciprocal in order to make it a normal fraction and ended up with ((1-x)(1-4)/(3-7)(x^2-x))

Simplifying the right-side: %281%2Fx+%2B+4%2Fx%5E2%29%2F%283-%287%2Fx%29%29, we get:

%281%2Fx+%2B+4%2Fx%5E2%29 ÷ %283+-+7%2Fx%29

%281%2Fx+%2B+4%2Fx%5E2%29 ÷ %283%2F1+-+7%2Fx%29

%28x+%2B+4%29%2Fx%5E2 ÷ %283x+-+7%29%2Fx ----- Multiplying 1st expression by LCD, x%5E2, and 2nd, by LCD, x

%28x+%2B+4%29%2Fx%5E2 * x%2F%283x+-+7%29 ------ Changing ÷ to * and inverting DIVISOR

%28x+%2B+4%29%2Fcross%28x%5E2%29x * cross%28x%29%2F%283x+-+7%29 ------- %28x+%2B+4%29%2F%28x%283x+-+7%29%29 ------- highlight_green%28%28x+%2B+4%29%2F%283x%5E2+-+7x%29%29