Greetings all, can someone explain to me how to find the constant of a and b for which [tex]\frac{a}{x+b}[/tex]+[tex]\frac{2}{x-4}[/tex]=[tex]\frac{3x}{(x+b)(x-4)}[/tex]
You add fractions by getting a "common denominator". Here the denominators are x+ b and x- 4. So you need to multiply both numerator and denominator of the first fraction by x+ b and the second fraction by x- 4.
That gives [tex]\frac{a(x+b)}{(x+b)(x-4)}+ \frac{2(x-4)}{(x+b)(x-4)}= \frac{(a+2)x+ ab-4}{(x+b)(x-4)}= \frac{3x}{(x+b)(x-4)}[/tex]. Can you finish?