Which expression is equal to 2x/x−2−x+5/x+3 ?

a. x^2+11x−6/(x−2)(x+3)

b. x^2+9x+6/(x−2)(x+3)

c. 3x^2+11x+6/(x−2)(x+3)

d. x^2+3x+10/(x−2)(x+3) i think is the correct answer.

, !

D is correct

Step-by-step explanation:

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

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

2x^2+6x/(x-2)(x+3)-(x^2+3x-10)(x+3)(x-2)

(x^2+3x+10)/(x+3)(x-2)

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

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