2 years ago

Dividing rational expressions

1 answer:

5 0

$\bf \textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)\\\\
-----------------------------\\\\
\cfrac{x+3}{x^2-2x}\cdot \cfrac{(x-2)^2}{x^2-9}\implies \cfrac{x+3}{x^2-2x}\cdot \cfrac{(x-2)(x-2)}{x^2-3^2}
\\\\\\
\cfrac{x+3}{x(x-2)}\cdot \cfrac{(x-2)(x-2)}{x^2-3^2}\implies \cfrac{\underline{x+3}}{x\underline{(x-2)}}\cdot \cfrac{\underline{(x-2)}(x-2)}{(x-3)\underline{(x+3)}}
\\\\\\
\cfrac{x-2}{x(x-3)}\iff\cfrac{x-2}{x^2-3x}$

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Graph the six terms of a finite series where a1 = −3 and r = 1.5.

s344n2d4d5 [400]

We are given the first term and the common ratio, this means they belong to a geometric series.

For the given series:

$a_{1}=-3 \\ 
r=1.5$

Each term of the geometric series is obtained by multiplying the previous term by common ratio.

So the next terms will be:

-4.5, -6.75, -10.125, -15.1875, -22.78125

The general formula for the G.P would be:

$a_{n}=-3(1.5)^{n-1}$

On plotting the series, the result will be like this: