Which expression is equivalent to the following complex fraction?

StartFraction negative 2 Over x EndFraction + StartFraction 5 Over y EndFraction divided by StartFraction 3 Over y EndFraction minus StartFraction 2 Over x EndFraction
StartFraction negative 2 y + 5 x Over 3 x minus 2 y EndFraction
StartFraction 3 x minus 2 y Over negative 2 y + 5 x EndFraction
StartFraction x squared y squared Over (negative 2 y + 5 x) (3 x minus 2 y) EndFraction
StartFraction (negative 2 y + 5 x) (3 x minus 2 y) Over x squared y squared EndFraction

Equivalent expressions are expressions that have equal values

The equivalent of the complex fraction is

The complex fraction is given as:

Start by taking the LCMs of the expressions in the brackets

Rewrite the fraction as follows:

Express the division as a product

Cancel out common factors

Rewrite as:

Hence, the equivalent of the complex fraction is

Read more about equivalent expressions at:

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  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

a = 11 : 4

b = 38

c = 1 for every 6