Find the Domain ((6x+5)/(2x+7))/((4x)/5-3/4)

Problem

Domain of (6*x+5)/(2*x+7)/((4*x)/5−3/4)

Solution

1. Identify the conditions for the domain of a rational expression. The domain consists of all real numbers except those that make any denominator in the expression equal to zero.

2. Set the denominator of the inner fraction in the numerator to zero.

2*x+7=0

2*x=−7

x=−7/2

3. Set the denominator of the entire complex fraction to zero.

(4*x)/5−3/4=0

(4*x)/5=3/4

16*x=15

x=15/16

4. Exclude these values from the set of all real numbers. The values x=−7/2 and x=15/16 must be excluded to prevent division by zero.

Final Answer

Domain: *{[x∈ℝ,x≠−7/2,x≠15/16]}

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