10x^2-3x-3= A(x^2+1)+(Bx+C) (x-1)
find A B C
y=kx-5
y=6x-x^2-6
solve for k
the factors which multiply with in the right side should equal to the factor of in the left side so you will have
and the factors which are multiply with x in the right side should equal to the factor with x in the left side so you will have
and finally the terms with no x in the right side should equal to the terms with no x in the left side so you will have this
now you have three equation with three variables so you can solve them
find the sum of the second and the third
find the sum of this and the first one
the rest for you
Multiply out the right side: .
In order that these be equal for all x, corresponding coefficients must be equal: 10= A+ B, -3= C- B, and -3= -C. Solve for A, B, and C.
. Because the left side does not have an " " term, there is NO value of k that will make this true for all x.y=kx-5
y=6x-x^2-6
solve for k