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Gre4nikov [31]
4 years ago
5

Rational equation for x, 3x/x+1 + 4/x-2=3

Mathematics
1 answer:
zimovet [89]4 years ago
5 0

Answer:

x = - 10

Step-by-step explanation:

Express the fractions on the left side as a single fraction.

Multiply the numerator/denominator of the first fraction by (x - 2)

Multiply the numerator/denominator of the second fraction by (x + 1)

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

Distribute the numerators and simplify

\frac{3x^2-6x+4x+4}{(x+1)(x-2)} = 3 ( cross- multiply )

3x² - 2x + 4 = 3(x+ 1)(x - 2) ← distribute

3x² - 2x + 4 = 3(x² - x - 2)

3x² - 2x + 4 = 3x² - 3x - 6 ( subtract 3x² - 3x  from both sides )

x + 4 = - 6 ( subtract 4 from both sides )

x = - 10

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