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Vadim26 [7]
3 years ago
15

Please help!! The question is the image below VVV Answers are also images after the picture.

Mathematics
1 answer:
Hatshy [7]3 years ago
4 0

Step-by-step explanation:

When adding two fractions with different bases (bottom numbers), we can use this function:

\frac{a}{b} + \frac{c}{d} = \frac{ad + cb}{bd}

So, to apply this to the given question:

\frac{x+3}{x-6} +\frac{1}{x-2}

= \frac{(x+3)(x-2)+(1)(x-6)}{(x-6)(x-2)}

From the given answers, we see we don't need to simplify the resulting base number, which makes things a lot easier.

  • Multiply top using: (a + b)(c + d) = ac + ad + bc + bd

= \frac{[(x*x) + (x*-2)+(3*x)+(3*-2)]+(x-6)}{(x-6)(x-2)}

  • Simplify.

= \frac{[x^2 -2x+3x-6]+(x-6)}{(x-6)(x-2)}

  • Remove parentheses.

= \frac{x^2 -2x+3x-6+x-6}{(x-6)(x-2)}

  • Simplify again.

= \frac{x^2 +2x-12}{(x-6)(x-2)}

Now if we wanna be a little smart, we can see that from here, the only answer that has x^2 and something else, is A. But, just for show, lets factor.

  • Factor.

= \frac{x(x+2)}{(x-6)(x-2)}

Answer:

A) \frac{x(x+2)}{(x-6)(x-2)}

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