Polynomial Factoring

Simplifying Rational Expressions


Simplify x2+11x+18x+2÷x+912.\frac{x^2+11x+18}{x+2} \div \frac{x+9}{12}.

(For all these problems you can automatically assume only values of xx which do not cause division by zero are used.)

If x+2x2+5x6×x26x+53x+6=xcax+b,\frac{x+2}{x^2+5x-6} \times \frac{x^2-6x+5}{3x+6} = \frac{x-c}{ax+b}, where aa, bb and cc are constants, what is a+b+ca+b+c?

If 35x4y33a8b7÷5x6y521a9b8=pabxmyn,\frac{35x^{4}y^{3}}{3a^{8}b^{7}} \div \frac{5x^{6}y^{5}}{21a^{9}b^{8}} = \frac{pab}{x^my^n}, where pp, mm and nn are constants, what is the value of p+m+np+m+n?

Simplify 4x2+20x+213x+6×2x+32x+7÷4x2+12x+96x+12.\frac{4x^2+20x+21}{3x+6} \times \frac{2x+3}{2x+7} \div \frac{4x^2+12x+9}{6x+12}.

If xx7xx+9=ax(x7)(x+9),\frac{x}{x-7}-\frac{x}{x+9}=\frac{ax}{(x-7)(x+9)},

holds for all values of xx, what is the value of aa?


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