Question 1167522
<pre>
Instead of doing yours for you, I'll do one exactly like yours step by step so
you can use it as a model to do yours by.  I'll do this one:
</pre>Find constants A and B such that
(x + 31)/(x^2 - 7x - 12) = A/(x - 4) + B(x + 3)
for all x such that x is not equal to -3 and x is not equal to 4. Give your
answer as the ordered pair (A,B).<pre>

{{{(x + 31)/(x^2 - 7x - 12)}}}{{{""=""}}}

{{{(x+31)/((x - 4)(x + 3))}}}{{{""=""}}}{{{A/(x - 4) + B/(x + 3)}}}

{{{(x+31)/((x - 4)(x + 1))}}}{{{""=""}}}{{{(A(x + 3) + B(x - 4))/((x - 4)(x + 3))}}}

These will be identical if and only if the numerators are identical:

{{{x+31}}}{{{""=""}}}{{{A(x + 3) + B(x - 4)}}}

Let x=-3 to cause x + 3 to become 0

It is OK to use x = -3 here because this is only to cause the numerators
to become equivalent.  It is not allowing x to be -3 in the original
expression.

{{{-3+31}}}{{{""=""}}}{{{A(-3 + 3) + B(-3 - 4)}}}

{{{28}}}{{{""=""}}}{{{-7B}}}

{{{-4}}}{{{""=""}}}{{{B}}}

Let x=4

Similarly, it is OK to use x = 4 here because this is only to cause the
numerators to become equivalent.  It is not allowing x to be 4 in the original
expression.

{{{4+31}}}{{{""=""}}}{{{A(4 + 3) + B(4 - 4)}}}

{{{35}}}{{{""=""}}}{{{7A}}}

{{{5}}}{{{""=""}}}{{{A}}}

{{{(x+31)/((x - 4)(x + 3))}}}{{{""=""}}}{{{5/(x - 24) + (-4)/(x + 3)}}}

(A,B) = (5,-4)

Now do yours the exact same way.

Edwin</pre>