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Question

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


(8r2+26rs+15s²)/25s²-4r²

 

 

Answer 1

(8r²+26rs+15s²)/(25s²-4r²)

 

NUMERATOR:

8r² + 26rs + 15s²

Let's try to factor by grouping.

Multiply the coefficient of the r² term

by the coefficient of the s² term:

8(15) = 120

We need to find factors of 120 that add

to the coefficient, 26, of the rs term.

6(20) = 120, 6+20 = 26

Separate 26rs out to 6rs + 20rs

 

8r² + 26rs +15s²

= 8r²+6rs+20rs+15s²

Grouping this for factoring

(8r²+6rs) + (20rs + 15s²)

= 2r(4r+3s) + 5s(4r+3s)

= (2r+5s)(4r+3s)

 

DENOMINATOR:

25s²-4r²

This looks like the difference of two squares.

25s² = (5s)² and 4r² = (2r)² so

25s²-4r²= (5s)²-(2r)² = (5s-2r)(5s+2r)

 

Putting back together:

 

(8r²+26rs+15s²)/(25s²-4r²)

= (2r+5s)(4r+3s)/(5s-2r)(5s+2r)

Cancelling out the common factor of 5s+2r we have

 

(4r+3s)/(5s-2r)