Thực hiện các phép cộng, trừ phân thức sau: x/x+2 - x/x-2

Giải SBT Toán 8 Bài 6: Cộng, trừ phân thức

Bài 3 trang 22 SBT Toán 8 Tập 1:Thực hiện các phép cộng, trừ phân thức sau:

a)$\frac{x}{x+2}-\frac{x}{x-2}$;

b)$\frac{3x}{2y}+\frac{5x}{3y}$;

c)$\frac{y-1}{5y}-\frac{3x-1}{15x}$;

d)$\frac{1-x}{x^3}+\frac{1}{x^2}$;

e)$\frac{x-2y}{x{y}^2}-\frac{y-2x}{x^{2}y}$;

g)$\frac{1-y^2}{3xy}+\frac{2y^3-1}{6x{y}^2}$.

Lời giải:

a)$\frac{x}{x+2}-\frac{x}{x-2}=\frac{x\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}-\frac{x\left(x+2\right)}{\left(x+2\right)\left(x-2\right)}$

$=\frac{x^2-2x-x^2-2x}{\left(x+2\right)\left(x-2\right)}=\frac{-4x}{\left(x+2\right)\left(x-2\right)}$.

b)$\frac{3x}{2y}+\frac{5x}{3y}=\frac{3x.3}{2y.3}+\frac{5x.2}{3y.2}=\frac{9x+10x}{6y}=\frac{19x}{6y}$.

c)$\frac{y-1}{5y}-\frac{3x-1}{15x}=\frac{\left(y-1\right).3x}{5y.3x}-\frac{\left(3x-1\right).y}{15x.y}$

$=\frac{3xy-3x-\left(3xy-y\right)}{15xy}=\frac{3xy-3x-3xy+y}{15xy}=\frac{y-3x}{15xy}$.

d)$\frac{1-x}{x^3}+\frac{1}{x^2}=\frac{1-x}{x^3}+\frac{1.x}{x^2.x}=\frac{1-x+x}{x^3}=\frac{1}{x^3}$.

e)$\frac{x-2y}{x{y}^2}-\frac{y-2x}{x^{2}y}=\frac{\left(x-2y\right).x}{x{y}^2.x}-\frac{\left(y-2x\right).y}{x^{2}y.y}$

$=\frac{x^2-2xy-y^2+2xy}{x^2{y}^2}=\frac{x^2-y^2}{x^2{y}^2}$.

g)$\frac{1-y^2}{3xy}+\frac{2y^3-1}{6x{y}^2}=\frac{\left(1-y^2\right).2y}{3xy.2y}+\frac{2y^3-1}{6x{y}^2}$

$=\frac{2y-2y^3+2y^3-1}{6x{y}^2}=\frac{2y-1}{6x{y}^2}$.