Réponse :
Les * sont des multiplications.
Pour les additions on met sur les mêmes dénominateurs :
[tex]\frac{a}{1} + \frac{b}{4} = \frac{4a}{4} + \frac{b}{4} = \frac{4a+b}{4}[/tex]
Pour les multiplications : [tex]\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}[/tex]
Pour les divisions : [tex]\frac{a}{b} / \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} =\frac{a \times d}{b \times c}[/tex]
Explications étape par étape
1) 3 + 13/4 = 3/1 +13/4
Donc (3*4 / 1*4) +13/4 = 12/4 +13/4 = 25/4
2) -10/16 +48/8 = -10/16 +96/16 = 86/16 =43/8
3) -12/14 - 18/7 -12/21 = -36/42 - 108/42 - 24/42 = -168/42 = -4
4) 37/2 - 108/30 = 555/30 - 108/30 = 447/30 = 149/10
5) 4*2/3 = 8/3
6) 12*5/3 = 60/3 = 20
7) 6/7 *3 = 18/7
8) 6/8 * 3/9 = 18/72 = 1/4
9) 7/9 * 2/5 = 14/45
10) 9/4 * 16/3 = 144/12 =12
11) 36/45 * 5/9 = 180/405 = 4/9
12) (48/35) / (16/7) = 48/35 * 7/16 = 336/560 = 3/5
13) a/b + c/d = (ad + cb) /bd
(50/81) + (100/63) = (50*63 +100*81)/(81*63) = 11250/5103 = 1250/567
14) [tex]\frac{x^{2}-1}{x-1}[/tex] déjà réduit au maximum.
15) 4*2/3 = 8/3
16)[tex]\frac{x}{x+1} - \frac{x}{x-1} = \frac{x(x-1) -x(x+1)}{(x+1)(x-1)} = \frac{x^{2}-x-x^{2}-x}{x^{2}-1} = \frac{-2x}{x^{2}-1}[/tex]
17) x-3 +4/x = x² -3x +4
18) (12/5) / (24/10) = 12/5 * 10/24 = 120/120 = 1
On peut aussi faire 24/10 = 12/5
(12/5) / (12/5) = 1
19) (8/5) / (3/7) = 8/5 * 7/3 = 56/15
20) (5/6)² = (5/6)*(5/6) = 25/36
