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Lady_Fox [76]
2 years ago
15

Im having trouble with this question... please help me.

Mathematics
2 answers:
Vesnalui [34]2 years ago
4 0

Answer:

\boxed{\sf \frac{3x - 11}{ {x}^{2}  + 2x - 3}}

Step-by-step explanation:

\sf \implies \frac{5}{x + 3}  -  \frac{2}{x - 1}  \\  \\  \sf Put \:  each \:  term  \: in \: \frac{5}{x + 3}  -  \frac{2}{x - 1} \: over  \: the  \: common  \\  \sf denominator \:(x + 3)(x - 1) :  \\  \sf  \implies \frac{5(x - 1)}{(x - 1)(x + 3)}    -   \frac{2(x + 3)}{(x - 1)(x + 3)}  \\  \\  \sf \frac{5(x - 1)}{(x - 1)(x + 3)}   -  \frac{2(x + 3)}{(x - 1)(x + 3)} =  \frac{5(x - 1)  -  2(x + 3)}{(x - 1)(x + 3)}  :  \\  \sf \implies \frac{5(x - 1)  -  2(x + 3)}{(x - 1)(x + 3)} \\  \\  \sf 5(x - 1) = 5x - 5 :  \\  \sf \implies  \frac{ \boxed{ \sf 5x - 5} - 2(x + 3)}{(x - 1)(x + 3)}  \\  \\  \sf  - 2(x + 3) =  - 2x - 6 :  \\  \sf \implies \frac{5x - 5  + \boxed{ \sf  - 2x - 6}}{(x - 1)(x + 3)}  \\  \\ \sf Grouping  \: like \:  terms, \: 5x  - 5 - 2x - 6 =  \\  \sf (5x - 2x) + ( - 5 - 6) :  \\  \sf \implies \frac{ \boxed{ \sf (5x - 2x) + ( - 5 - 6)}}{(x - 1)(x + 3)}  \\  \\  \sf 5x - 2x = 3x :  \\  \sf \implies \frac{ \boxed{ \sf 3x} + ( - 5 - 6)}{(x - 1)(x + 3)}  \\  \\ \sf  - 5 - 6 =  - 11 :  \\  \sf \implies \frac{3x +  \boxed{ - 11}}{(x - 1)(x + 3)}

\sf (x - 1)(x + 3) = x(x + 3) - 1(x + 3) :  \\  \sf \implies \frac{3x - 11}{ \boxed{ \sf x(x + 3) - 1(x + 3)}}  \\  \\ \sf x(x + 3) =  {x}^{2}  + 3x :  \\  \sf \implies \frac{3x - 11}{  \boxed{ \sf {x}^{2}  + 3x} - 1(x + 3)}  \\  \\  \sf  - 1(x + 3) =  - x - 3 \\  \sf \implies \frac{3x - 11}{ {x}^{2} + 3x +  \boxed{ \sf - x - 3} }  \\  \\  \sf 3x - x = 2x :  \\  \sf \implies \frac{3x - 11}{ {x}^{2}  + 2x - 3}

kompoz [17]2 years ago
3 0

Answer:

last option.

Step-by-step explanation:

See attached.

I'm not sure why you crossed out the last option, but it seems to be correct.

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