SOLUTION: What values for x must be excluded in the following fraction? x-3/(4x-5)(x+1)

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Question 112192: What values for x must be excluded in the following fraction? x-3/(4x-5)(x+1)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=%28x-3%29%2F%284x%5E2-x-5%29 Start with the given function


4x%5E2-x-5=0 Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain.




%284x-5%29%28x%2B1%29=0 Factor the left side (note: if you need help with factoring, check out this solver)




Now set each factor equal to zero:

4x-5=0 or x%2B1=0

x=5%2F4 or x=-1 Now solve for x in each case


So our solutions are x=5%2F4 or x=-1



Since x=-1 and x=5%2F4 make the denominator equal to zero, this means we must exclude x=-1 and x=5%2F4 from our domain