about algebraic fraction 6Q20點

1.
3r / (r - s) - 3s / (r - s)
= (3r - 3s) / (r - s)
= 3(r - s) / (r - s)
= 3


2.
[a / (1 - b)] ÷ [a³ /(2 - 2b)]
= [a / (1 - b)] ÷ [a³ /2(1 - b)]
= [a / (1 - b)] x [2(1 - b) / a³]
= [2a(1 - b)] / [a³(1 - b)]
= 2/a²


3.
[(6m - 12n) / 2n] x [2n² /(2n - m)]
= [6(m - 2n) / 2n] x [-2n² /(m - 2n)]
= [-12n²(m - 2n)] / [2n(m - 2n)]
= -6n


4.
(3m + 6mn) / 6mn
= [3m(1 + 2n)] / 6mn
= (1 + 2n) / 2n


5.
(-4m² / 12n³) x (9n / 6m)
= -36m³n / 72mn³
= -m² / 2n²


6.
[x / (y - x)] - [3x / (x - y)]
= [x / (y - x)] + [3x / (y - x)]
= 4x / (y - x)