Simplify ( square root of x+5-3)/(x-4)

Problem

(√(,x+5)−3)/(x−4)

Solution

1. Identify the indeterminate form by substituting x=4 into the expression, which results in 0/0

2. Rationalize the numerator by multiplying both the numerator and the denominator by the conjugate of the numerator, which is √(,x+5)+3

3. Expand the numerator using the difference of squares formula (a−b)*(a+b)=a2−b2

(√(,x+5)−3)*(√(,x+5)+3)=(x+5)−9

4. Simplify the numerator by combining like terms.

(x+5)−9=x−4

5. Rewrite the entire expression with the simplified numerator and the factored denominator.

(x−4)/((x−4)*(√(,x+5)+3))

6. Cancel the common factor of x−4 from both the numerator and the denominator, assuming x≠4

1/(√(,x+5)+3)

Final Answer

(√(,x+5)−3)/(x−4)=1/(√(,x+5)+3)

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