Question

question 1: build the fraction x+5/x+3 to an equivalent fraction whoes denominator is x^2

question 2: simplify (x^2+6x+9)(3-x)/(x-3)(2x+6)

question 3. find the product in simplest from x^3-9x/x^5+27x^2 * x^2-3x+9/x^2+3x

Answer 1

First, observe the rule of operator precedence, i.e. BEDMAS (brackets,exponents, division/multiplication, addition/subtration) in that order.

Q1.
I suspect the expression should have been written as (x+5)/(x+3) to be interpreted correctly.

Based on that, we know that the new denominator is x², and denote the new numerator as N, then equate the two equivalent fractions:

(x+5)/(x+3) = N / x²

Cross multiply and solve for N:
N = (x+5)*x²/(x+3)
=(x³+4x²)/(x+3)
Unfortunately N is not a polynomial.

For Q2 and Q3, I suggest you correct the expressions according to the BEDMAS precedence rules and repost.

Answer 2

typo:
N = (x+5)*x²/(x+3)
=(x³+5x²)/(x+3)