Answer:
[tex]x^{2}[/tex]+5x+4
Step-by-step explanation:
First, we must determine that the equation we need to solve is
p(x)-q(x)
Now we can substitute these values to make an equation we can solve
This will look like
([tex]x^{2}[/tex]-1)-5(x-1)
First, lets start by simplifying -5(x-1)
We need to multiply 5 by both terms in the parenthesis. This will equal
-5x+5
Now we can insert that back into our original equation of ([tex]x^{2}[/tex]-1)-5(x-1) which will now look like
([tex]x^{2}[/tex]-1)- -5x+5
Now we can see that there is a minus -5 which would be the same as a + 5
So we can change the sign to be +
([tex]x^{2}[/tex]-1)+5x+5
Now we can combine like terms (-1 and 5) to make this easier to solve
This will look like
[tex]x^{2}[/tex]+(-1+5)+5x
We can simplify this equation by adding -1 to 5 which equals 4
So our new equation is
[tex]x^{2}[/tex]+4+5x
Now all we need to do is put it in standard form to look like
[tex]x^{2}[/tex]+5x+4
And this is our answer
