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春耕一片田地,甲队单独进行a天可以完成,乙队单独进行b天可以完成。甲、乙两队合耕几天可以完成? 设甲、乙两队合耕x天可以完成,那末 1/x=1/a+1/b 两根导线的电阻分别是R_1和R_2,则其总电阻R满足等式 1/R=1/R_1+1/R_2。物体、象和焦点到透镜的距离这三个量之间有下列关系: 1/f+1/q=1/h。以上三个实际问题反映到数学中来,就是研究x_1,x_2,x_3这三个正量之间的下列关系: 1/x_3=1/x_1+1/x_2。(*) 在等式(*)中,如果x_1,x_2两个量已知,那么我们可以用解分式方程的方法,解得 x=x_1x_2/(x_1+x_2)。(*′)
Spring plowing a field, A team can complete a day alone, B team can complete b days. How can two teams a and b be completed in a few days? A and b can be completed in two days together. Then the resistances of the two wires 1/x=1/a+1/b are R_1 and R_2, respectively. The total resistance R satisfies the equation 1/R=1/R_1+1/R_2. The following relationship between the three objects: object, image, and distance from the focus to the lens: 1/f+1/q=1/h. The above three practical problems are reflected in mathematics, that is, to study the following relationships between the three positive quantities x_1, x_2, and x_3: 1/x_3=1/x_1+1/x_2. (*) In equation (*), if the two quantities x_1, x_2 are known, then we can solve x=x_1x_2/(x_1+x_2) by solving the fractional equation. (*’)