Question

Rational Expressions and Equations

Find all real solutions. Be sure to check for extraneous solutions. Show all work and steps.

3y-1/ y^2 + 1 = 1

y = 1, 2

Answer 1

3y -1 y2 + 1 = 1

cross multiply by following idea

if

= C

then a= bc

so

3y-1=1(y²+1)

3y-1= y² +1

on rewriting

y²-3y+2= 0

now factor left term y²-3y+2.

rewrite -3y as -y-2y

y²-y -2y+2

take y outside from fist two and -2 from last two

y (y-1) -2(y-1)

now y-1 is common term .take it outside and re write

(y-1)(y-2).

now we factored it. so

y²-3y+2=(y-1)(y-2).

(y-1)(y-2).=0

this become zero when

y-1=0 or y-2=0

so

y=1 or y=2

now lets check the solution. given expression is a rational equation . if a solution for rational equation make denominater zero, then this is extrenius solution .

both y=1 or y=2 not make denominator y²+1 zero . so the are not extranius.

so solution are

y= 1 ,2