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finding ranges of binomial expansions?

find the range of values of x for which the binomial expansion of 3+9x/(1+x)(3+5x) is valid?

how do i do these questions helllllppp pleeeassseee thankuuu :smile:

Reply 1

ugk4life

i need help for this too

Reply 2

sabna93

awww lols someone help us .....

Reply 3

navennn

3+9x/(1+x)(3+5x)

I assume you would have had to expand (1+x)^-1 or similar and (3+5x)^-1, which is: 3^-1(1+5/3x)^-1

Now when expanding, the 'x' term has to be |x|=<1 ( -1 =< x =< 1)

Therefore in the (1+x) term, the range is |x| =< 1
In the (1+5/3x) term, the range is |5/3x| =< 1, multiply both sides by 5/3 implies that |x| =< 3/5

Therefore the range of x is that |x| =< 1 and |x| =< 3/5. The second inequality implies the first one also, so you don't need to worry about that. Therefore, the range of binomial expansions is |x| =< 3/5.

Hope that helped, I know it was a long explanation for a simple thing but better to understand then to just know. I may have done something blatantly wrong, but its 10 :colondollar: