Divide Simplify If Possible $$\frac { x ^ { 2 } - 2 x + x y - 2 y } { 9 x ^ { 2 } - 9 y ^ { 2 } } \div \frac { x - 2 } { 12 x - 12 y }$$

question 75

Multiple Choice

Divide. Simplify if possible.
- $$\frac { x ^ { 2 } - 2 x + x y - 2 y } { 9 x ^ { 2 } - 9 y ^ { 2 } } \div \frac { x - 2 } { 12 x - 12 y }$$

• A) \(\frac { 12 \left( x ^ { 2 } - 2 x + x y - 2 y \right) } { 9 ( x + y ) ( x - 2 ) }\)
• B) 1
• C) \(\frac { 4 } { 3 }\)
• D) \(\frac { ( x - 2 ) ^ { 2 } } { 108 ( x - y ) ^ { 2 } }\)

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Definitions:

Common Variance

The shared variance between variables in a statistical model, often referring to the portion of variability that is accounted for by a common factor.

Degrees of Freedom

The number of independent values or quantities which can be assigned to a statistical distribution, typically in the context of parameters estimated from sample data.

Pooled-Variance T Test

A statistical test that compares the means of two independent samples while assuming that they have the same variance.

Pooled Variance

The weighted average of variances from two or more groups, assuming that these groups have the same variance.