State the restrictions and then simplify

Question

State the restrictions and then simplify:

8x^2+2x-15

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2x^2+15x+18

 

 

 

 

 

 

 

Answer 1

8x^2+2x-15

8*15=2*2*2*3*5=(2*2*3)*(2*5)=12*10 and 12-10=2

factor the numerator

(4x-5)(2x+3)

2x^2+2x+18

2*18=2*2*3*3=(2*2*3)*(3)=12*3 and 12+3=15

factor the denominator

(2x+3)(x+6)

x≠-6 and x≠-3/2

factor out (2x+3) from both terms

(4x-5)/(x+6) is the answer