help me with solving this?

Question

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


(5r²+23r+12)/(25r²-9)

 

i have no idea how to factor these as Five does't go into 23 or 12. what do i do?

Answer 1

Hi Jay,

 

 

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


(5r²+23r+12)/(25r²-9)

 

 

5r²+23r+12

 

The tried and true method for factoring trinomials when there is a coefficient greater than 1 for the 1st term is called Double Slide.

 

Start by multiplying the coefficient of the 1st term by the last term.

5r²+23r+12

r²+23r+12(5)

r²+23r+60    

 

Since the last term in positive, both factors must have the same sign.

since the 2nd term is positive, then both factors must be positive.

 

So we need factors of 60 which sum 23

 

1     60   no

2    30    no

3     20   YES   3+20=23

 

r²+23r+60

(r+3)(r+20)

 

Since we multiplied before by 5, now we have to divide by five and reduce

(r+3/5)(r+20/5)

(r+3/5)(r+4)    Since 3/5 cannot be further reduce, we Slide the 5 in front of the r.

(5r+3)(r+4)

 

Now for the denominator

(25r²-9)

since both terms are perfect squares, then a²-b²=(a+b)(a-b)

 

(5r+3)(5r-3)

 

The original problem

(5r²+23r+12)/(25r²-9)

 

 

(5r+3)(r+4)

------------

(5r+3)(5r-3)

 

The factor 5r+3 can cancel out which leaves

 

(r+4)
------

(5r-3)

 

I hope this helps you understand the process.