Answer:
1. [tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 1}}}}}[/tex]
2. [tex] \boxed{ \bold{ \huge{ \boxed{ \sf{n = - 5}}}}}[/tex]
Step-by-step explanation:
1. [tex] \sf{ \frac{6}{x + 1} = \frac{3}{x} }[/tex]
Do cross multiplication
[tex] \dashrightarrow{ \sf{6x = 3(x + 1)}}[/tex]
Distribute 3 through the parentheses
[tex] \dashrightarrow{ \sf{6x = 3x + 3}}[/tex]
Move 3x to left hand side and change it's sign
[tex] \dashrightarrow{ \sf{6x - 3x = 3}}[/tex]
Collect like terms
[tex] \dashrightarrow{ \sf{3x = 3}}[/tex]
Divide both sides by 3
[tex] \dashrightarrow{ \sf{ \frac{3x}{3} = \frac{3}{3} }}[/tex]
Calculate
[tex] \dashrightarrow{ \sf{x = 1}}[/tex]
The value of x is 1
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2. [tex] \sf{ \frac{2}{6} = \frac{2n + 8}{n - 1}} [/tex]
Do cross multiplication
[tex] \dashrightarrow{ \sf{2(n - 1) = 6(2n + 8)}}[/tex]
Distribute 2 through the parentheses
Similarly, distribute 6 through the parentheses
[tex] \dashrightarrow{ \sf{2n - 2 = 12n + 48}}[/tex]
Move 12n to left hand side and change it's sign
Similarly, move 48 to right hand side and change it's sign
[tex] \dashrightarrow{ \sf{2n - 12n = 48 + 2}}[/tex]
Collect like terms
[tex] \dashrightarrow{ \sf{ - 10n = 48 + 2}}[/tex]
Add the numbers : 48 and 2
[tex] \dashrightarrow{ \sf{ - 10n = 50}}[/tex]
Divide both sides by -10
[tex] \dashrightarrow{ \sf{ \frac{ - 10n}{ - 10} = \frac{50}{ - 10} }}[/tex]
Calculate
[tex] \dashrightarrow{ \sf{n = - 5}}[/tex]
The value of n is -5 .
Hope I helped!
Best regards! :D
