I am struggling with this, as silly as it seems. The difficult\"calculator\" alg

Question

I am struggling with this, as silly as it seems. The difficult"calculator" algebra is working fine with me but this stuff mightas well be chinese. Can someone please walk me through the easiestways to solve these? example-1/2 (one half) + 2/x (2 over x) = 1/3+3/x x=6(according to the back of my books answer key, my issue is WHY isit 6) or the square root 3x-4=1 I am struggling with this, as silly as it seems. The difficult"calculator" algebra is working fine with me but this stuff mightas well be chinese. Can someone please walk me through the easiestways to solve these? example-1/2 (one half) + 2/x (2 over x) = 1/3+3/x x=6(according to the back of my books answer key, my issue is WHY isit 6) or the square root 3x-4=1

Explanation / Answer

- +- = - + - 2 x 3 x
The first step in these kind of problems where there are twofractions is to find a common denominator.
x+4 x+9 --- = ---- 2x 3x
Once you do it, you want to simplify the equation as much aspossible. This may involve cross-multiplying and any other toolsyou have learned.
3x^2+12x = 2x^2+18x
After that, you want to move everything to one side.
x^2 -6x = 0
Simplify if you can. If not, use the quadratic equation or anyother tools you need. For this instance, you can factor out an x.
x(x-6) = 0
Then, solve.
x = 0, x = 6

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