Answer:
A = 13 , B = - 43 , C = 13
Step-by-step explanation:
Consider the left side
[tex]\frac{3x - 5}{4x+3}[/tex] + [tex]\frac{-2x+1}{7x-2}[/tex]
= [tex]\frac{(3x-5)(7x-2)+(-2x+1)(4x+3)}{(4x+3)(7x-2)}[/tex] ← expand factors on numerator using FOIL
= [tex]\frac{21x^2-41x+10-8x^2-2x+3}{(4x+3)(7x-2)}[/tex]
= [tex]\frac{13x^2-43x+13}{(4x+3)(7x-2)}[/tex]
The denominators on both sides of the equation are equal so equate the numerators.
13x² - 43x + 13 = Ax² + Bx + C
comparing coefficients of like terms , gives
A = 13 , B = - 43 , C = 13
