SOLUTION: 1.) 8-2x / 5x+10 = blank / 5y(x+2) 2.) 3x^2+10x+3 / x-1 = x(x+3)(x+5)(3x+1) / blank What is in the blank? Thank you.

Hi,        

The 'blank' is used for the request to place in it an appropriate response:

For ex: 8-2x / 5x+10 = blank / 5y(x+2) 

'performing operations on left side of equal sign to reach the right side denominator'

8-2x / 5x+10   |Simplifying

2(4-x) / 5(x+2)  |Multiplying both numerator and denominator by y

2y(4-x) / 5y(x+2)  | One would put 2y(4-x) in the 'blank' for the numerator



ex: 3x^2+10x+3 / x-1 = 3x^2+10x+3 / x-1 = x(x+3)(x+5)(3x+1) / blank

'performing operations on left side of equal sign to reach the right side numerator'



3x^2+10x+3 / x-1  |factoring the numerator

(3x + 1)(x+3) /(x-1) |Multiplying numerator and denominator by x(x+5)

(3x + 1)(x+3)x(x+5) /(x-1)x(x+5) OR x(x+3)(x+5)(3x + 1) /x(x-1)(x+5)

One would put x(x-1)(x+5) in the blank for the denominator