Answer:
Step-by-step explanation:
Fraction :x/y
numerator x = y - 2
Now the fraction can be written as: (y-2)/y
3 is added to both denominator and numerator.
After adding 3, the new fraction = [tex]\frac{y-2 +3 }{y + 3 } = \frac{y+ 1 }{y +3}[/tex]
The sum of the new fraction and the original fraction is 53/35
[tex]\frac{y+1}{y+3} + \frac{y-2}{y} = \frac{53}{35}\\\\\frac{(y+1)*y}{(y+3)*y}+\frac{(y-2)*(y+3)}{y(y+3)}=\frac{53}{35}\\\\\frac{y^{2}+y}{y^{2}+3y}+\frac{y^{2}+y-6}{y^{2}+3y}=\frac{53}{35}\\\\\frac{y^{2}+y+y^{2}+y-6}{y^{2}+3y}=\frac{53}{35}\\\\\frac{2y^{2} + 2y - 6}{y^{2}+3y}=\frac{53}{35}\\\\[/tex]
35*(2y² + 2y - 6) = 53 *(y² + 3y)
35*2y² + 2y * 35 - 6*35 = 53 *y² + 53*3y
70y² + 70y - 210 = 53y² + 159y
70y² + 70y - 210 - 53y² - 159y = 0
70y² - 53y² + 70y - 159y - 210 = 0
17y² - 89y - 210 = 0
Answer:
17y^2 - 89y - 210 = 0
Step-by-step explanation:
Original fraction: x/y
The numerator is 2 les than the denominator, x = y - 2
Original fraction: (y - 2)/y
New fraction:
Add 3 to the numerator and denominator of the original fraction:
(y - 2 + 3)/(y + 3) = (y + 1)/(y + 3)
Add the new fraction and old fraction and get 53/35.
(y - 2)/y + (y + 1)/(y + 3) = 53/35
35y(y + 3)[(y - 2)/y] + 35y(y + 3)[(y + 1)/(y + 3)] = 35y(y + 3)(53/35)
35(y + 3)(y - 2) + 35y(y + 1) = 53(y^2 + 3y)
35(y^2 + y - 6) + 35(y^2 + y) = 53y^2 + 159y
17y^2 - 89y - 210 = 0
