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rewona [7]
3 years ago
9

Solve the equation, using any method. Be sure to check for extraneous solutions.

Mathematics
1 answer:
hichkok12 [17]3 years ago
7 0

Answer: No real solution.

Step-by-step explanation:

\frac{2}{(2x+6)}-\frac{2}{x^2+5x+6}=\frac{3}{(x+3)}

First solve x^2+5x+6

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

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

\frac{[(2x+6)(x+2)]-(4x-12)}{(2x+6)(x+3)(x+2)} = \frac{3}{(x+3)}

\frac{(2x^2+4x+6x+12)-(4x-12)}{(2x+6)(x+3)(x+2)} = \frac{3}{(x+3)}

\frac{2x^2+10x+12-4x+12}{(2x+6)(x+3)(x+2)} = \frac{3}{(x+3)}

\frac{2x^2+6x+24}{(2x+6)(x+3)(x+2)} = \frac{3}{(x+3)}

Past this point, we can't solve 2x^2+6x+24 and obtain real values of x. Therefore, there are no real solutions.

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Answer:

The third option.

Step-by-step explanation:

(\frac{4xy^3}{x^2})^2\\\\=(\frac{4y^3}{x})^2\\\\=\frac{16y^6}{x^2}

Hence the 3rd option.

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