Question

Pleasee help with this question asap I’m begging y’all

Answer 1

Answer: a = 10

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Work Shown:

`y = (4x+30)/(x+5)\\\\y = (4x+20+10)/(x+5)\\\\y = ((4x+20)+10)/(x+5)\\\\y = (4(x+5)+10)/(x+5)\\\\y = (4(x+5))/(x+5)+(10)/(x+5)\\\\y = 4+(10)/(x+5)\\\\`

Therefore, a = 10

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As an alternative approach, we could work in reverse like this:

`y = 4+(a)/(x+5)\\\\y = 4*(x+5)/(x+5)+(a)/(x+5)\\\\y = (4(x+5))/(x+5)+(a)/(x+5)\\\\y = (4(x+5)+a)/(x+5)\\\\y = (4x+20+a)/(x+5)\\\\`

Then notice that the 20+a must be 30, so solving 20+a = 30 leads to a = 10

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As yet another alternative approach (well I suppose it's actually 2 extra approaches) we could use either polynomial long division or synthetic division. Either way, you should end up with a remainder of 10, which corresponds directly to a = 10