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)
[tex]\frac{3x(x-2)}{(x+1)(x-2)}[/tex] + [tex]\frac{4(x+1)}{(x+1)(x-2)}[/tex] = 3
Distribute the numerators and simplify
[tex]\frac{3x^2-6x+4x+4}{(x+1)(x-2)}[/tex] = 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
