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Determinants

Question
CBSEENMA12035727

If open vertical bar table row cell straight x plus 1 end cell cell space space straight x minus 1 end cell row cell straight x minus 3 end cell cell space straight x plus 2 end cell end table close vertical bar space equals space open vertical bar table row 4 cell space space minus 1 end cell row 1 cell space space space space 3 end cell end table close vertical bar comma then write the value of x. 

Solution
open vertical bar table row cell straight x plus 1 end cell cell space space straight x minus 1 end cell row cell straight x plus 3 end cell cell space straight x plus 2 end cell end table close vertical bar space equals space open vertical bar table row 4 cell space space minus 1 end cell row 1 cell space space space space 3 end cell end table close vertical bar
rightwards double arrow space space left parenthesis x plus 1 right parenthesis thin space left parenthesis straight x plus 2 right parenthesis space minus space left parenthesis straight x minus 1 right parenthesis thin space left parenthesis straight x minus 3 right parenthesis space equals space 12 plus 1
rightwards double arrow space straight x squared plus 3 straight x plus 2 minus straight x squared plus 4 straight x minus 3 space equals space 13
rightwards double arrow space space 7 straight x minus 1 space equals space 13
rightwards double arrow 7 straight x space equals space 14
rightwards double arrow space straight x space equals space 2

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