This is hard for me to understand

Question

Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answer box.


(12x²+11xy+2y²⁾/(y²-xy-20x²)

 

 

Answer 1

Michael,

what you need to do is try to factor out the numerator

and the denominator and then see what factors they

have in common.  Those common factors can be

cancelled out of the fraction in order to reduce the

rational expression to lowest terms.  Look at the

numerator and denominator separately, factor them,

then put the resulting equations back into fraction form.

 

NUMERATOR:

12x²+11xy+2y²

Let's try to factor by grouping.

12(2) = 24.  Look for factors of 24 that add to 11.

That would by 8*3.

Separate the 11xy into 8xy + 3xy and rewrite the numerator.

 

12x² + 8xy + 3xy + 2y²

Grouping:

(12x²+8xy)+(3xy+2y²)

= 4x(3x+2y) + y(3x+2y)

= (4x+y)(3x+2y)

 

DENOMINATOR:

y²-xy-20x²

First, let's put the variables in the same order as

they appeared in the numerator:

-20x²-xy+y²

Factors of -20 that add to -1 are (-5)(4).

Replace -xy with -5xy + 4xy

-20x² - 5xy + 4xy + y²

Grouping these:

(-20x²-5xy) + (4xy+y²)

= -5x(4x+y) + y(4x+y)

= (-5x+y)(4x+y)

 

Put the fraction back together:

 

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

Cancelling out the common factor of (4x+y)

 

= (3x+2y)/(-5x+y)