Find the Domain (6x+5)/(2x+7)

Problem

(6*x+5)/(2*x+7)

Solution

1. Identify the type of function. This is a rational function, which is defined for all real numbers except where the denominator is equal to zero.

2. Set the denominator equal to zero to find the excluded values of x

2*x+7=0

3. Solve for x by subtracting 7 from both sides.

2*x=−7

4. Divide both sides by 2 to isolate x

x=−7/2

5. State the domain as all real numbers except the value that makes the denominator zero. In interval notation, this excludes −7/2

Final Answer

Domain:(−∞,−7/2)∪(−7/2,∞)

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