求解 (x+2y)(x+4y)/(x-2y)(x-5y)divx^2-16y^2/x^2-10xy+25y^2

$$\frac { ( x + 2 y ) ( x + 4 y ) } { ( x - 2 y ) ( x - 5 y ) } \div \frac { x ^ { 2 } - 16 y ^ { 2 } } { x ^ { 2 } - 10 x y + 25 y ^ { 2 } }$$

求值

$$\frac{\left(x-5y\right)\left(x+2y\right)}{\left(x-2y\right)\left(x-4y\right)}$$

简短求解步骤

\frac{\left(x+2y\right)\left(x+4y\right)}{\left(x-2y\right)\left(x-5y\right)} 除以 \frac{x^{2}-16y^{2}}{x^{2}-10xy+25y^{2}} 的计算方法是用 \frac{\left(x+2y\right)\left(x+4y\right)}{\left(x-2y\right)\left(x-5y\right)} 乘以 \frac{x^{2}-16y^{2}}{x^{2}-10xy+25y^{2}} 的倒数。

$$\frac{\left(x+2y\right)\left(x+4y\right)\left(x^{2}-10xy+25y^{2}\right)}{\left(x-2y\right)\left(x-5y\right)\left(x^{2}-16y^{2}\right)}$$

将尚未因式分解的表达式分解因式。

$$\frac{\left(x+2y\right)\left(x+4y\right)\left(x-5y\right)^{2}}{\left(x-5y\right)\left(x-4y\right)\left(x-2y\right)\left(x+4y\right)}$$

消去分子和分母中的 \left(x-5y\right)\left(x+4y\right)。

$$\frac{\left(x-5y\right)\left(x+2y\right)}{\left(x-4y\right)\left(x-2y\right)}$$

展开表达式。

$$\frac{x^{2}-3xy-10y^{2}}{x^{2}-6xy+8y^{2}}$$

展开

$$\frac{10y^{2}+3xy-x^{2}}{\left(x-2y\right)\left(4y-x\right)}$$

简短求解步骤

\frac{\left(x+2y\right)\left(x+4y\right)}{\left(x-2y\right)\left(x-5y\right)} 除以 \frac{x^{2}-16y^{2}}{x^{2}-10xy+25y^{2}} 的计算方法是用 \frac{\left(x+2y\right)\left(x+4y\right)}{\left(x-2y\right)\left(x-5y\right)} 乘以 \frac{x^{2}-16y^{2}}{x^{2}-10xy+25y^{2}} 的倒数。

$$\frac{\left(x+2y\right)\left(x+4y\right)\left(x^{2}-10xy+25y^{2}\right)}{\left(x-2y\right)\left(x-5y\right)\left(x^{2}-16y^{2}\right)}$$

将尚未因式分解的表达式分解因式。

$$\frac{\left(x+2y\right)\left(x+4y\right)\left(x-5y\right)^{2}}{\left(x-5y\right)\left(x-4y\right)\left(x-2y\right)\left(x+4y\right)}$$

消去分子和分母中的 \left(x-5y\right)\left(x+4y\right)。

$$\frac{\left(x-5y\right)\left(x+2y\right)}{\left(x-4y\right)\left(x-2y\right)}$$

展开表达式。

$$\frac{x^{2}-3xy-10y^{2}}{x^{2}-6xy+8y^{2}}$$