(x^2+5x-36)/(x^2-16)
=(x^2+9x-4x-36)/(x^2-4^2)
=x(x+9)-4(x+9)/(x+4)(x-4)
=(x-4)(x+9)/(x+4)(x-4)
=x+9/x+4
Hope this helps.
Answer:
A, C, D, E
Step-by-step explanation:
According to the rational root theorem, any rational roots will be of the form ...
±(divisor of the constant)/(divisor of the leading coefficient)
The constant is 8, and its divisors are 1, 2, 4, 8.
The leading coefficient is 6, and its divisors are 1, 2, 3, 6.
So, no rational root will have 3 in the numerator, eliminating choices B and F. The remaining choices are possible rational roots:
A^3
a to the power of three
Answer: choice C) -15x^4y
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Explanation:
The coefficients are -3 and 5. They are the numbers to the left of the variable terms
Multiply the coefficients to get -3*5 = -15. So -15 is the coefficient in the answer
Multiply the x terms to get x^3 times x = x^(3+1) = x^4. Notice the exponents are being added
Do the same for the y terms as well: y^2 times y^(-1) = y^(2+(-1)) = y^(2-1) = y^1 = y
So we have a final coefficient of -15, the x terms simplify to x^4 and the y terms simplify to just y
Put this all together and we end up with -15x^4y which is what choice C is showing
