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Question

Answer 1

Step 1:

The inequality is .

Determine the real zeros ( -intercepts of the graph )of and the real numbers for which is undefined.

The zeroes of the function are the values of for which .

The function is .

Rewrite the function in lowest terms .

The zeroes of the numerator are and .

A rational function is undefined when denominator is zero.

is undefined for .

Step 2:

Use the zeros and undefined values found in Step 1 to divide the real number line into intervals.

Denominator of the function should not be zero.

The function is defined for all values of except at .

The function intervals are .

Step 3:

Select a number in each interval, evaluate at the number, and determine whether is positive or negative.

If is positive, all values of in the interval are positive. If is negative, all values of in the interval are negative.

.

The real zero of numerator is  ,  and the real zeros of denominator .

So the real zeros are divide the - axis into four intervals.

The function intervals are .

Comments

Continued...

Step 4:

Choosing a number for in each interval and evaluating .

The solution of algebraical inequality are in the intervals , and .

Solution:

Option (a) is correct.