Question

Answer 1

\(1,\\ a,=5x-x^2+x^2-9=5x-9\\ b,=x^2-6x+9-x^2+x+2=-5x+11\\ c,=\dfrac{x+1+x-1}{\left(x-1\right)\left(x+1\right)}=\dfrac{2x}{x^2-1}\\ 2,\\ a,=2ab\left(a^2+2ab+3b^2\right)\\ b,=\left(x-y\right)^2-25=\left(x-y-5\right)\left(x-y+5\right)\\ c,=x\left(4x^2-7x-2\right)=x\left(4x^2-8x+x-2\right)\\ =x\left(4x+1\right)\left(x-2\right)\)

\(3,\\ a,\Leftrightarrow x^2-16+6x-x^2=2\\ \Leftrightarrow6x=18\Leftrightarrow x=3\\ b,\Leftrightarrow x^2+x-6-\left(x-1\right)^3:\left(x-1\right)=2\\ \Leftrightarrow x^2+x-6-\left(x-1\right)^2=2\\ \Leftrightarrow x^2+x-6-x^2+2x-1=2\\ \Leftrightarrow3x=9\Leftrightarrow x=3\)