Resolve the following rational expressions into partial fractions.
\({{x^2+x+1}\over{x^2-5x+6}}\)

Determine the region in the plane determined by the inequalities.
\(2x+3y\le 6,\ x+4y\le 4,\ x\ge 0,\ y\ge 0.\)

Determine the region in the plane determined by the inequalities.
\(x-2y\ge 0,\ 2x-y\le -2,\ x\ge 0,\ y\ge 0.\)

Resolve the following rational expressions into partial fractions.
\({{x+12}\over{(x+1)^{2}(x-2)}}\)

Resolve the following rational expressions into partial fractions.
\({{7+x}\over{(1+x)(1+x^2)}}\)

Find the condition that one of the roots of ax²+bx+c may be reciprocal of the other.

Find a quadratic polynomial f(x) such that, f(0) = 1; f(-2) = 0 and f(1) = 0.

Construct a cubic polynomial function with rational coefficients having zeros at x = \(\frac{2}{5},1+\sqrt{3}\) such that f(0)=-8

Use the method of undetermined coefficients to find the sum of 1 + 2 + 3 +....+ (n - 1) + n, n ∈ N

Find the square root of 7-4\(\sqrt{3}\)