MHB Simplify and state any restrictions on the variables.

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The discussion focuses on simplifying the expression $$\frac{2(x+1)}{3} ⋅ \frac{x-1}{6(x+1)}$$ and identifying restrictions on the variable. The initial simplification attempt incorrectly reduced the expression without fully simplifying the fraction $$\frac{2}{18}$$. A key mistake was not recognizing that the term $(x+1)$ in the denominator leads to division by zero when $x = -1$. The correct restrictions on the variable are that $x$ cannot equal -1, ensuring the expression remains defined. The final simplified expression should be correctly calculated to avoid errors.
eleventhxhour
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Simplify and state any restrictions on the variables:

$$\frac{2(x+1)}{3} ⋅ \frac{x-1}{6(x+1)} $$

This is what I did, which is wrong (according to the textbook).

$$\frac{2}{3} ⋅ \frac{x-1}{6}$$

$$\frac{2x-2}{18}$$

$$\frac{2(x-1)}{18}$$

Can someone tell me what I've done wrong? Also, how would you find the restrictions?

Thanks.
 
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It appears that you simply did not simplify fully...what is:

$$\frac{2}{18}$$

fully reduced?

In the original expression, what value of $x$ will cause division by zero?
 
Ohh, I see. That was a simple mistake.
Thanks!
And the restriction would be -1.
 
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