How do I sketch the graph y= (2x+5)/(x-1)
Say you want to simplify
then you would multiply the first constant by the highest common denominator so you can put it all in one fraction as so:
and then simplify and you get
But what if you started with this expression and wanted to go back to the start now?
You need to cancel out the x in the numerator so you need to convert it into the form
Notice that the numerator has 4x in it so a=2 so that we can have this 4x.
Now in order to keep the numerator the same we need a number b so that it makes [itex]2(2x+1)+b=4x+5[/itex] and once you solve this you get b=3.
Then we get
From this expression we can easily sketch the graph
by noting that there is a vertical asymptote at 2x+1=0, x=-1/2 and there is a horizontal asymptote at y=2 (since the fraction never equals 0).
Now see if you can apply the same idea to your problem.
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