Home > Algebra > Addition and Subtraction of Rational Expressions

How do you simplify # (y+2)/(y-5)-(y-4)/(y+3)#?

Answer 1

Hazel Anglin

#color(blue)(=>(14*(y-1)) /( (y-5)(y+3))#

#(y+2)/(y-5) - (y-4) / (y+3)#

L C M #(y-5) (y+3)#

#=>( (y+2)(y+3) - (y-4)(y-5))/ ((y-5)(y+3))#

#=>(y^2 + 5y + 6 - y^2 + 9y - 20) /( (y-5)(y+3))#

#=>(14y - 14) /( (y-5)(y+3))#

#color(blue)(=>(14*(y-1)) /( (y-5)(y+3))#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Savannah Anderson

To simplify the expression (y+2)/(y-5)-(y-4)/(y+3), we need to find a common denominator for the two fractions. The common denominator is (y-5)(y+3).

Next, we can rewrite the fractions with the common denominator:

[(y+2)(y+3)]/[(y-5)(y+3)] - [(y-4)(y-5)]/[(y-5)(y+3)]

Expanding the numerators, we get:

[(y^2 + 5y + 6)]/[(y-5)(y+3)] - [(y^2 - 9y + 20)]/[(y-5)(y+3)]

Now, we can combine the fractions by subtracting the numerators:

[(y^2 + 5y + 6) - (y^2 - 9y + 20)]/[(y-5)(y+3)]

Simplifying the numerator:

[y^2 + 5y + 6 - y^2 + 9y - 20]/[(y-5)(y+3)]

Combining like terms:

[14y - 14]/[(y-5)(y+3)]

Factoring out 14 from the numerator:

14(y - 1)/[(y-5)(y+3)]

Therefore, the simplified expression is 14(y - 1)/[(y-5)(y+3)].

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.