Simplify and state any restrictions on the variables.

In summary, Simplifying variables involves reducing an expression or equation to its simplest form by combining like terms and eliminating any unnecessary elements. Restrictions on variables should be stated when there are certain values or conditions that must be met in order for the expression or equation to be valid. Examples of restrictions on variables include a variable being limited to positive values, a variable being excluded from certain values that would make the expression undefined, or a variable being constrained to a specific range of values. Restrictions on variables can affect the solution by limiting the possible values that the variable can take, thus narrowing down the potential solutions. In some cases, restrictions may also lead to no solution or an infinite number of solutions. Yes, restrictions on variables can change the meaning of an expression or
  • #1
eleventhxhour
74
0
Simplify and state any restrictions on the variables:

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

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

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

\(\displaystyle \frac{2x-2}{18}\)

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

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

Thanks.
 
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  • #2
It appears that you simply did not simplify fully...what is:

\(\displaystyle \frac{2}{18}\)

fully reduced?

In the original expression, what value of $x$ will cause division by zero?
 
  • #3
Ohh, I see. That was a simple mistake.
Thanks!
And the restriction would be -1.
 

FAQ: Simplify and state any restrictions on the variables.

What does it mean to simplify variables?

Simplifying variables involves reducing an expression or equation to its simplest form by combining like terms and eliminating any unnecessary elements.

How do I know when to state restrictions on variables?

Restrictions on variables should be stated when there are certain values or conditions that must be met in order for the expression or equation to be valid. This could be due to limitations in the domain or restrictions on the values of the variables.

What are some examples of restrictions on variables?

Examples of restrictions on variables include a variable being limited to positive values, a variable being excluded from certain values that would make the expression undefined, or a variable being constrained to a specific range of values.

How do restrictions on variables affect the solution of an expression or equation?

Restrictions on variables can affect the solution by limiting the possible values that the variable can take, thus narrowing down the potential solutions. In some cases, restrictions may also lead to no solution or an infinite number of solutions.

Can restrictions on variables change the meaning of an expression or equation?

Yes, restrictions on variables can change the meaning of an expression or equation by limiting the scope of the variables and altering the range of possible solutions. It is important to be mindful of restrictions when simplifying or solving equations to ensure the correct interpretation of the final result.

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