Question

Answer 1

a: \(\frac{A}{2x-1}=\frac{6x^2+3x}{4x^2-1}\)

=>\(\frac{A}{2x-1}=\frac{3x\left(2x+1\right)}{\left(2x+1\right)\left(2x-1\right)}=\frac{3x}{2x-1}\)

=>A=3x

b: \(\frac{4x^2-3x-7}{A}=\frac{4x-7}{2x+3}\)

=>\(\frac{4x^2-7x+4x-7}{A}=\frac{4x-7}{2x+3}\)

=>\(\frac{\left(4x-7\right)\left(x+1\right)}{A}=\frac{4x-7}{2x+3}\)

=>\(A=\frac{\left(4x-7\right)\left(x+1\right)\left(2x+3\right)}{4x-7}=\left(x+1\right)\left(2x+3\right)\)

=>\(A=2x^2+3x+2x+3=2x^2+5x+3\)