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Svetach [21]
2 years ago
7

Find the simplified quotient. (2x^2 + 5x +3 / x^2 - 3x -4) / (4x^2 + 2x - 6 / x^2 - 8x + 16)

Mathematics
2 answers:
irinina [24]2 years ago
8 0

ANSWER

\frac{x - 4}{2x - 2}

EXPLANATION

The given expression is;

\frac{2 {x}^{2}  + 5x + 3}{ {x}^{2}  - 3x - 4}  \div  \frac{4 {x}^{2}  + 2x - 6}{ {x}^{2}  - 8x + 16}

We factor to obtain;

\frac{(x + 1)(2x + 3)}{(x - 4)(x + 1)}  \div  \frac{2(x - 1)(2x + 3)}{(x - 4)(x - 4)}

Multiply by the reciprocal of the second fraction

\frac{(x + 1)(2x + 3)}{(x - 4)(x + 1)}  \times \frac{(x - 4)(x - 4)}{2(x - 1)(2x + 3)}

Cancel out common factors to get,

\frac{1}{1}  \times \frac{(x - 4)}{2(x - 1)}

\frac{x - 4}{2x - 2}

PIT_PIT [208]2 years ago
7 0

Answer:

X-4/2x-2

Step-by-step explanation:

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