Bài 44:
\(a,3x+15=3\left(x+5\right)\\ x^2-25=\left(x-5\right)\left(x+5\right)\\ \Rightarrow MC:3\left(x+5\right)\left(x-5\right)\\ Ta.có:\dfrac{5}{3x+15}=\dfrac{5\left(x-5\right)}{3\left(x+5\right)\left(x-5\right)}=\dfrac{5x-25}{3\left(x+5\right)\left(x-5\right)}\\ \dfrac{3}{x^2-25}=\dfrac{3}{\left(x-5\right)\left(x+5\right)}=\dfrac{3.3}{3.\left(x-5\right)\left(x+5\right)}=\dfrac{9}{3\left(x-5\right)\left(x+5\right)}\)
Bài 44:
\(b,x^2-1=\left(x-1\right)\left(x+1\right)\\ x^3+2x^2+x=x\left(x^2+2x+1\right)=x\left(x+1\right)^2\\ Ta.có:\dfrac{x^2-x}{x^2-1}=\dfrac{x\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}=\dfrac{x}{x+1}\\ \dfrac{3x+3}{x^3+2x^2+x}=\dfrac{3\left(x+1\right)}{x.\left(x+1\right)^2}=\dfrac{3}{x\left(x+1\right)}\\ \dfrac{2x}{x^3}=\dfrac{2}{x^2}\\ \Rightarrow MC:x^2\left(x+1\right)\\ Ta.có:\dfrac{x^2-x}{x^2-1}=\dfrac{x}{x+1}=\dfrac{x.x^2}{x^2\left(x+1\right)}=\dfrac{x^3}{x^2\left(x+1\right)}\\ \dfrac{3x+3}{x^3+2x^2+x}=\dfrac{3}{x\left(x+1\right)}=\dfrac{3x}{x^2\left(x+1\right)}\\ \dfrac{2x}{x^3}=\dfrac{2}{x^2}=\dfrac{2\left(x+1\right)}{x^2\left(x+1\right)}=\dfrac{2x+2}{x^2\left(x+1\right)}\)
Bài 43:
\(a,BCNN\left(12;18;6\right)=36\\ MC:36x^2y^2z^2\\ Ta.có:\dfrac{-7y}{12xz^2}=\dfrac{-7y.x.y^2.3}{36x^2y^2z^2}=\dfrac{-21xy^3}{36x^2y^2z^2}\\ \dfrac{11z}{18x^2y}=\dfrac{11z.y.z^2.2}{36x^2y^2z^2}=\dfrac{22yz^3}{36x^2y^2z^2}\\ \dfrac{5x}{6y^2z}=\dfrac{5x.x^2.z.6}{36x^2y^2z^2}=\dfrac{30x^3z}{36x^2y^2z^2}\)
\(b,BCNN\left(7;14\right)=14\\ MC:14x^2y^3z^3\\ Ta.có:\dfrac{6}{7xy^2z}=\dfrac{6.xyz^2.2}{14x^2y^3z^3}=\dfrac{12xyz^2}{14x^2y^3z^3}\\ \dfrac{11}{14x^2y^3z^3}=\dfrac{11}{14x^2y^3z^3}\)
Bài 44 :
a) \(\dfrac{5}{3x+15}=\dfrac{5}{3\left(x+5\right)}=\dfrac{5\left(x-5\right)}{3\left(x+5\right)\left(x-5\right)}=\dfrac{5x-25}{3\left(x^2-25\right)}\)
\(\dfrac{3}{x^2-25}=\dfrac{9}{3\left(x^2-25\right)}\)
b) \(\dfrac{x^2-x}{x^2-1}=\dfrac{x\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}=\dfrac{x}{x+1}\)
\(\dfrac{3x+3}{x^3+2x+x}=\dfrac{3\left(x+1\right)}{x\left(x^2+2x+1\right)}=\dfrac{3\left(x+1\right)}{x\left(x+1\right)^2}=\dfrac{3}{x\left(x+1\right)}\)
\(\dfrac{2x}{x^3}=\dfrac{2}{x^2}\)
\(MSC=x^2\left(x+1\right)\)
\(\dfrac{x^2-x}{x^2-1}=\dfrac{x\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}=\dfrac{x}{x+1}=\dfrac{x^3}{x^2\left(x+1\right)}\)
\(\dfrac{3x+3}{x^3+2x+x}=\dfrac{3\left(x+1\right)}{x\left(x^2+2x+1\right)}=\dfrac{3\left(x+1\right)}{x\left(x+1\right)^2}=\dfrac{3}{x\left(x+1\right)}=\dfrac{3x}{x^2\left(x+1\right)}\)
\(\dfrac{2x}{x^3}=\dfrac{2\left(x+1\right)}{x^2\left(x+1\right)}=\dfrac{2x+2}{x^2\left(x+1\right)}\)
Bài 42:
\(a,Ta.có:\dfrac{3x}{9x^2y}=\dfrac{3x:3x}{9x^2y:3x}=\dfrac{1}{3xy}\\ MC:6xy^3\\ Ta.có:\dfrac{2x+1}{6xy^3}=\dfrac{2x+1}{6xy^3};\dfrac{1}{3xy}=\dfrac{1.2y^2}{3xy.2y^2}=\dfrac{2y^2}{6xy^3}\\ ---\\ b,x^2-25=\left(x-5\right)\left(x+5\right)\\ \Rightarrow MC:\left(x+5\right)\left(x-5\right)\\ Ta.có:\dfrac{3x^2-4x+1}{x^2-25}=\dfrac{3x^2-4x+1}{\left(x-5\right)\left(x+5\right)}\\ \dfrac{x-3}{5-x}=\dfrac{3-x}{x-5}=\dfrac{\left(3-x\right)\left(x+5\right)}{\left(x-5\right)\left(x+5\right)}=\dfrac{15-2x-x^2}{\left(x-5\right)\left(x+5\right)}\\ \dfrac{4x}{x+5}=\dfrac{4x\left(x-5\right)}{\left(x-5\right)\left(x+5\right)}=\dfrac{4x^2-20x}{\left(x-5\right)\left(x+5\right)}\)
