Algebra Session 1 | In-class question

GRE Quant Problem Solving
1

Hi Guys,
I was just solving this one question in Algebra Part 1 video where we are comparing:

1/x to (x+1)/x^2

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Screen Shot 2023-03-26 at 3.18.27 PM1190×359 135 KB

How I thought about this is that I cancelled 1/x from both sides. On the left we then had 0 and on the right we had (x+1)/x. Now if I take a negative value of x here, quantity a becomes bigger.

Where did I go wrong?

2

Not in itself a mistake, but

is where you went wrong. If you “cancel” x from both sides by multiplying both quantities by x (which needs to be done very carefully due to inequalities flipping when x is negative and isn’t what I would recommend), you’ll get 1 as Quantity A, not 0.

If by “cancelling” you meant subtracting both quantities by 1/x, Quantity B would be

\frac{x + 1}{x^2} - \frac{1}{x}
=\frac{x}{x^2} + \frac{1}{x^2} - \frac{1}{x}
=\frac{1}{x} + \frac{1}{x^2} - \frac{1}{x}
=\frac{1}{x^2}