What is the domain of the rational function f of x is equal to 2 x over the quantity 2 x cubed minus 5 x squared minus 12 x end quantity x is an element of all real numbers such that x is not equal to 0
x is an element of all real numbers such that x is not equal to negative three halves comma 4
x is an element of all real numbers such that x is not equal to 0 comma negative three halves comma 4
x is an element of all real numbers such that x is not equal to 0 comma three halves comma negative 4

Using the domain concept, it is found that the domain of the function is: x is an element of all real numbers such that , second option.

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The function is:

The points outside the domain are the zeros of , which we find solving a quadratic equation.

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Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

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This polynomial has roots such that , given by the following formulas:

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is a quadratic equation with .

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The domain is: x is an element of all real numbers such that , second option.

A similar problem is given at

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1

answer: 0.26

i used the calculator on google