Multiply and simplify x2+2x−3x2+1x−20x−1x+5

Question

Multiply and simplify  x2+2x−3x2+1x−20x−1x+5

Corgnatiui · Accepted Answer

Step 1  Firstly, we will factorise  the quadratics by splitting middle terms  x2+2x−3=x2+3x−x−3=x(x+3)−1(x+3)=(x−1)(x+3)  x2+x−20=x2+5x−4x−20=x(x+5)−4(x+5)=(x−4)(x+5)  Stpe 2  Now we will replace the quadratic by their factors and reciprocate the lower fraction.  x2+2x−3x2+x−20÷x−1x+5=(x−1)(x+3)(x−4)(x+5)×(x+5)(x−1)=x+3x−4  Answer: x+3x−4

Paul Mitchell · Accepted Answer

Step 1  x2+2x−3x2+1x−20÷x−1x+5  Divide x2×2+2x−3x2+1x−20 by x−1x+5 by multiplying x2×2+2x−3x2+1x−20 by the reciprocal of x−1x+5  (x2×2+2x−3)(x+5)(x2+1x−20)(x−1)  Factor the expressions that are not already factored.  2(x+5)(x−(−127−12))(x−(127−12))(x−4)(x−1)(x+5)  Cancel out x+5 in both numerator and denominator  2(x−(−127−12))(x−(127−12))(x−4)(x−1)  Expand the expression.  2x2+2x−3x2−5x+4

RizerMix · Accepted Answer

Step 1 x2+2x−3x2+1×x−20x−1x+5 Apply rule: a×1=a =x2+2x−3x2+x−20x−1x+5 Apply the fraction rule: abcd=a×db×c =(x2+2x−3)(x+5)(x2+x−20)(x−1) Cancel: (x2+2x−3)(x+5)(x2+x−20)(x−1): x+3x−4

Multiply and simplify \frac{\frac{x^{2}+2x-3}{x^{2}+1x-20}}{\frac{x-1}{x+5}}

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