Quy đồng mẫu thức các phân thức sau:

a) $\frac{5}{2x+6}, \frac{3}{x^2-9}$;                 b) $\frac{2x}{x^2-8x+16}, \frac{x}{3x^2-12x}$;

Giải

a)

• Tìm MTC:
  • $2x+6=2(x+3)$
  • $x^2-9=(x-3)(x+3)$
  • MTC=$2(x-3)(x+3)$=$2\left(x^2-9\right)$
• Nhân tử phụ:
  • $2(x-3)(x+3): 2(x+3)=(x-3)$
  • $2(x-3)(x+3): x^2-9=2$
• Quy đồng:
  • $\frac{5}{2x+6}=\frac{5.(x-3)}{2\left(x+3\right)}=\frac{5(x-3)}{2(x-3)(x+3)}$
  • $\frac{3}{x^2-9}=\frac{3}{\left(x-3\right)\left(x+3\right)}=\frac{3.2}{2.\left(x-3\right)\left(x+3\right)}=\frac{6}{2\left(x-3\right)\left(x+3\right)}$.

b) 

• Tìm MTC:
  • $x^2-8x+16 ={\left(x-4\right)}^2$
  • $3x^2-12x=3x\left(x-4\right)$
  • MTC=$3x{\left(x-4\right)}^2$
• Nhân tử phụ:
  • $3x{\left(x-4\right)}^2: {(x-4)}^2=3x$
  • $3x{\left(x-4\right)}^2: 3x\left(x-4\right)=\left(x-4\right)$
• Quy đồng:
  • $\frac{2x}{x^2-8x+16}=\frac{2x}{{\left(x-4\right)}^2}=\frac{2x.3x}{3x{\left(x-4\right)}^2}=\frac{6x^2}{3x{\left(x-4\right)}^2}$
  • $\frac{x}{3x^2-12x}=\frac{x}{3x\left(x-4\right)}=\frac{x\left(x-4\right)}{3x{\left(x-4\right)}^2}$.