Xover x squared minus 1 plus 10 over x minus 1 equals negative 4

The solutions:   x = -2x = -3/4======refresh if you see errors in the explanation.factor out the x²-1    if we want to add the fractions on the left side of the equation, we need a common denominator.consider  , which is    if we multiply the numerator and denominator of that fraction by  , then we will get a common denominator for the left side of the equation.    the denominators are the same. so we can combine the fractions.    distribute the 10, and then collect like terms.    multiply both sides of the equation by  to cancel out the denominator on the left side of the equation. then expand the right side.    can move all the terms to the left side.add  to both sides of the equation, then subtract 4 from both sides of the equation.    this is factorizable. find two numbers that → multiply to get 24 (the leading coefficient times the constant)→ add to get 11these two numbers are 8 and 3.  decompose the middle term, using 8x and 3x.then factor by grouping    if  or  , the equation will be true.so possible solutions are    ======check these solutions by substituting them into the original equation to see if they are true.    doing the same for x = -3/4 is also true.