What should be subtracted from \((\frac{2x^2+2x-7}{x^2+x-6})\) to ge

1.	What should be subtracted from \((\frac{2x^2+2x-7}{x^2+x-6})\) to get \((\frac{x-1}{x+2})\)A) \(\frac{x-2}{x-3}\)B) \(\frac{x^2+6x-11}{x^2+x-6}\)C) \(\frac{x+2}{x-3}\)D) \(\frac{x-2}{x+3}\)
Answer» Correct option is (B) \(\frac{x^2+6x-11}{x^2+x-6}\) Let p(x) should be subtracted from \(\left(\frac{2x^2+2x-7}{x^2+x-6}\right)\) to get \(\left(\frac{x-2}{x+3}\right)\) i.e., \(\frac{2x^2+2x-7}{x^2+x-6}-p(x)\) \(=\frac{x-2}{x+3}\) \(\Rightarrow\) \(p(x)=\frac{2x^2+2x-7}{x^2+x-6}\) \(-\frac{x-2}{x+3}\) \(=\frac{2x^2+2x-7-(x-2)^2}{(x+3)(x-2)}\) \(=\frac{2x^2+2x-7-x^2+4x-4}{(x-2)(x+3)}\) \(=\frac{x^2+6x-11}{x^2+x-6}\) Correct option is B) \(\frac{x^2+6x-11}{x^2+x-6}\)

What should be subtracted from \((\frac{2x^2+2x-7}{x^2+x-6})\) to get \((\frac{x-1}{x+2})\)A) \(\frac{x-2}{x-3}\)B) \(\frac{x^2+6x-11}{x^2+x-6}\)C) \(\frac{x+2}{x-3}\)D) \(\frac{x-2}{x+3}\)

Answer»

Correct option is (B) \(\frac{x^2+6x-11}{x^2+x-6}\)

Let p(x) should be subtracted from

\(\left(\frac{2x^2+2x-7}{x^2+x-6}\right)\) to get \(\left(\frac{x-2}{x+3}\right)\)

i.e., \(\frac{2x^2+2x-7}{x^2+x-6}-p(x)\) \(=\frac{x-2}{x+3}\)

\(\Rightarrow\) \(p(x)=\frac{2x^2+2x-7}{x^2+x-6}\) \(-\frac{x-2}{x+3}\)

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

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

\(=\frac{x^2+6x-11}{x^2+x-6}\)

Correct option is B) \(\frac{x^2+6x-11}{x^2+x-6}\)