Can someone please help me with this question:
'Solve the equation x2/x+1  5/x1 = 1/3..... Write your answer in the form p+/ q (square root) r, where p, q and r are natural numbers'
x2/x+1  5/x1 was the last question, and the answer was x(squared)8x3/x(squared)1.
I checked the answers, and the answer is x = 6+/2(square root)10. Id really appreciate some help, thanks.

Dazzla16
Hi maria! Here are the steps involved in solving that equation.
[(x2)/(x+1)]  [5/(x1)] = 1/3
Multiply both sides by 3:
[3(x2)/(x+1)]  [3(5)/(x1)] = 3(1/3)
[(3x6)/(x+1)]  [15/(x1)] = 1
Now you have to express the two fractions in the same denominator. To do this, multiply the numerator and the denominator of (3x6)/(x+1) by (x1) and multiply the numerator and the denominator of 15/(x1) by (x+1). You get:
[(3x^2  9x + 6)/(x^2  1)]  [(15x + 15)/(x^2  1)] = 1
You can subtract the two fractions from each other since they are expressed in the same denominator.
[(3x^2  24x  9)/(x^2  1)] = 1
Then, express 1 as a fraction.
[(3x^2  24x  9)/(x^2  1)] = 1/1
Cross multiply and you get:
3x^2  24x  9 = x^2  1
Make one side equal to 0:
2x^2  24x  8 = 0
Divide both sides by 2:
x^2  12x  4 = 0
Now use the quadratic formula. Remember to make a = 1, b = 12 and c = 4.
x = [b +/ sqrt(b^2  4ac)]/2a
x = [(12) +/ sqrt((12)^2  4(1)(4))]/2(1)
x = [12 +/ sqrt(160)]/2
Square root of 160 is simplified to 4sqrt(10).
x = [12 +/ 4sqrt(10)]/2
x = 6 +/ 2sqrt(10)
Hope it helps :)

ismisemaria
Hey, thanks that's a great help, just confused on what do you mean by 'sqrt of 160 is simplified to 4sqrt(10)', how is it simplified, as we haven't covered that in class yet

Dazzla16
Hi again. The simplification of surds is covered in the section on Indices. In order to simplify a number in surd form, you have to see if the surd can have one factor being a perfect square (such as 4, 9, 16, 25, etc.).
In our case, sqrt(160) can have a factor being a perfect square, which is sqrt(16).
sqrt(160) = sqrt(16) X sqrt(10)
We already know that the square root of 16 is equals to 4, so we replace sqrt(16) with 4.
sqrt(160) = 4 X sqrt(10)
sqrt(160) = 4sqrt(10)
Hope this helps :)

ismisemaria
Seriously thank you so much! This really helped!

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