Solve the inequality and graph it on the real number line: 5/x-1 - 2x/x+1 <  1   Thanks

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Inequality to be solved: (5/x-1) - (2x/(x+1) < 1 Multiply each term by common denominator (x-1)(x+1) to clear fractions: 5x - 5 - 2x² + 2 < x² - 1 Set right side to zero to set up quadratic inequality -3x² +5x - 2 < 0 Multiply each term by negative 1 get rid of negative sign in front of coefficient of x square term: 3x² - 5x + 2 > 0 Rewrite coefficient of x term as sum two factors of product of coefficient of x square term and constant term(factors of 6 (3 x 2) which add up to -5 are -6 and +1): 3x² + (-6 + 1)x - 2 > 0 Distribute x over terms in parens: 3x² - 6x + x - 2 > 0 Factor 1st terms and last 2 terms: 3x(x-2) + 1(x-2) > 0 Pull out common factor (x-2) from both terms to complete factoring: (3x-1)(x-2) > 0 Set each factor to zero to get critical points of x to set up number line regions: 3x - 1 = 0; x = 1/3x - 2= 0; x = +2 Use test points for (3x-1)(x-2) > 0 for testing a positive outcome for region of number line based  upon critical points of x:                                        x < 1/3        1/3 < x < 2        x > 2                                       use x = 0     use x = 1           use x = 3 3x-1                                -1 (-)            2 (+)                 8 (+)  x-2                                  -2 (-)           -1 (-)                 1 (+)------------------------------------------------------------------------------(3x-1)(x-2)                        2 (+)          -2 (-)                 8 (+)    Solution:  x < 1/3 or x > 2 Number Line:     1.  Shade region x < 1/3 with open circle at 1/3    2.  Shade region x > 2 with open circle at 2