Question

Can you help me, please? THANKS!

Answer 1

A = 13 , B = - 43 , C = 13

Explanation:

Consider the left side

`(3x - 5)/(4x+3)` +
`(-2x+1)/(7x-2)`

=
`((3x-5)(7x-2)+(-2x+1)(4x+3))/((4x+3)(7x-2))` ← expand factors on numerator using FOIL

=
`(21x^2-41x+10-8x^2-2x+3)/((4x+3)(7x-2))`

=
`(13x^2-43x+13)/((4x+3)(7x-2))`

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