Write a simplified expression for the area of the rectangle at the right. State all restrictions on a.

(3a+9)/(2a-6) by (4a+4)/(a+3)

Question

Write a simplified expression for the area of the rectangle at the right. State all restrictions on a.

(3a+9)/(2a-6)  by  (4a+4)/(a+3)

campbell_st · Answer

the values that a cannot take can be found by looking at the denominators in the dimensions

you need to solve 

2a - 6 = 0

and

a + 3 = 0

these values would result in the denominators of each fraction being zero, which is undefined. 

so to simplify the area you need to multiply

but first take out common factors

$$\frac{3(a + 3)}{2(a - 3)} \times \frac{4(a + 1)}{(a + 3)}$$


this will give

$$\frac{3( a + 3)\times 4(a + 1)}{2(a - 3)\times(a + 3)}$$

cancel any common factors... 

and then simplify

hope this helps.

anonymous · Answer

i am still not quite sure how to simplify that.

campbell_st · Answer

well what can you see that is in the numerator and denominator..?

anonymous · Answer

a+3 cancel, but then what?

campbell_st · Answer

there is another common factor as well...its 2

so you have $$\frac{3\times2(a + 1)}{(a - 3)}$$

can you simplify this... its just distributing the numerator

anonymous · Answer

but what happened to the 4 that was on the top

anonymous · Answer

of to get the 2 on the top it should have been 2(a+2) instead of 4(a+1)

anonymous · Answer

so its 3(a+2)/(a-3). is that simplified completely?

anonymous · Answer

What do you do next?? Gaahhh