Ask some mathematical questions about fractional equation Given that 1 / (x-1) = 2, what is the value of 2 / (x-1) + X-1? If the equation 1 / (x + 3) = 2 / (x + k) has a negative solution, then the range of K is? If (x-3) / (X-2) and (2-x) / (3x + 2) are reciprocal, what is the value of X? Given that the solution of the equation [2 (x + a)] / [a (x-1)] = - 8 / 5 is x = - 1 / 5, what is the value of a? | Math enthusiast | Mathematical art

Ask some mathematical questions about fractional equation Given that 1 / (x-1) = 2, what is the value of 2 / (x-1) + X-1? If the equation 1 / (x + 3) = 2 / (x + k) has a negative solution, then the range of K is? If (x-3) / (X-2) and (2-x) / (3x + 2) are reciprocal, what is the value of X? Given that the solution of the equation [2 (x + a)] / [a (x-1)] = - 8 / 5 is x = - 1 / 5, what is the value of a?

solution
∵1/(x-1)=2
∴x-1=1/2
2/(x-1)+x-1
=2×1/(x-1)+(x-1)
=2×2+1/2
=4+1/2
=9/2
1 / (x + 3) = 2 / (x + k) has negative solution
Multiply both sides by (x + 3) (x + k)
∴x+k=2(x+3)
That is, x + k = 2x + 6
∴x=k-6

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