Toán Lớp 8: Tính và rút gọn biểu thức: a) x²-5x+6/x²+7x+12 : x²-4x+4/x²+3x b) x²-2xy+y²/x²-xy+y² : x-y/x³+y³

Question

Toán Lớp 8:  Tính và rút gọn biểu thức: a) x²-5x+6/x²+7x+12 : x²-4x+4/x²+3x b) x²-2xy+y²/x²-xy+y² : x-y/x³+y³

lanthuhoa · Answer

Giải đáp:     a) {x^2 - 3x}/{x^2 + 2x - 8}     b) x^2 - y^2     Lời giải và giải thích chi tiết:    a)   {x^2 - 5x + 6}/{x^2 + 7x + 12} : {x^2 - 4x + 4}/{x^2 + 3x}   = {x^2 - 2x - 3x + 6}/{x^2 + 3x + 4x + 12} : {x^2 - 2.x.2 + 2^2}/{x(x + 3)}   = {(x^2 - 2x) - (3x - 6)}/{(x^2 + 3x) + (4x + 12)} : {(x - 2)^2}/{x(x + 3)}   = {x(x - 2) - 3(x - 2)}/{x(x + 3) + 4(x + 3)} : {(x - 2)^2}/{x(x + 3)}   = {(x - 2)(x - 3)}/{(x + 3)(x + 4)} : {(x - 2)^2}/{x(x + 3)}   = {(x - 2)(x - 3)}/{(x + 3)(x + 4)} . {x(x + 3)}/{(x - 2)^2}   = {x - 3}/{x + 4} . {x}/{x - 2}   = {x(x - 3)}/{(x + 4)(x - 2)}   = {x^2 - 3x}/{x^2 - 2x + 4x - 8}   = {x^2 - 3x}/{x^2 + 2x - 8}   $  $   b)   {x^2 - 2xy + y^2}/{x^2 - xy + y^2} : {x - y}/{x^3 + y^3}   = {(x - y)^2}/{x^2 - xy + y^2} : {x - y}/{(x + y)(x^2 - xy + y^2)}   = {(x - y)^2}/{x^2 - xy + y^2} . {(x + y)(x^2 - xy + y^2)}/{x - y}   = {x - y}/1 . {x + y}/{1}   = (x - y)(x + y)   = x^2 - y^2   #SunHee

phuongthaongoc · Answer

Giải đáp + Lời giải và giải thích chi tiết:

a) $\dfrac{x^2 – 5x + 6}{x^2 + 7x + 12} : \dfrac{x^2 – 4x + 4}{x^2 + 3x}$

$= \dfrac{(x – 2)(x – 3)}{(x + 3)(x + 4)} : \dfrac{(x – 2)^2}{x(x + 3)}$

$= \dfrac{(x – 2)(x – 3)}{(x + 3)(x + 4)} . \dfrac{x(x + 3)}{(x – 2)^2}$

$= \dfrac{x – 3}{x + 4} . \dfrac{x}{x – 2}$

$= \dfrac{x(x – 3)}{(x + 4)(x – 2)}$

$= \dfrac{x^2 – 3x}{x^2 + 2x – 8}$

b) $\dfrac{x^2 – 2xy + y^2}{x^2 – xy + y^2} : \dfrac{x – y}{x^3 + y^3}$

$= \dfrac{(x – y)^2}{x^2 – xy + y^2} : \dfrac{x – y}{(x + y)(x^2 – xy +y^2)}$

$= \dfrac{(x – y)^2}{x^2 – xy + y^2} . \dfrac{(x + y)(x^2 – xy +y^2)}{x – y}$

$= \dfrac{x – y}{1} . \dfrac{x + y}{1}$

$= (x – y)(x + y) = x^2 – y^2$