Please

Please determine the solvability conditions of the equation, solve the equation and perform the test:

x divided by x squared minus 2x plus1 the whole minus x + 3 divided by x squared minus 1 this is equal to 0:

x/(x²-2x+1) - (x+3)/( x²-1) = 0

Correct result:

x =  3

Solution:

$$\begin{gathered} {\displaystyle \frac{x}{x^2-2x+1}}-{\displaystyle \frac{x+3}{x^2-1}}=0 \\ {k}^2-2k+1=0 \\ {k}^2-2k+1=0 \\ {k}^2-2k+1=0 \\ a=1;b=-2;c=1 \\ D=b^2-4ac=2^2-4\cdot 1\cdot 1=0 \\ D=0 \\ {k}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{2\pm \sqrt{0}}{2}}=1\pm \sqrt{0} \\ {k}_{1,2}=1\pm 0 \\ {k}_1=k_2=1 \\ \text{ Factored form of the equation: } \\ (k-1)(k-1)=0 \\ {q}^2-1=0 \\ {q}^2-1=0 \\ {q}^2-1=0 \\ a=1;b=0;c=-1 \\ D=b^2-4ac=0^2-4\cdot 1\cdot (-1)=4 \\ D>0 \\ {q}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{\pm \sqrt{4}}{2}} \\ {q}_{1,2}={\displaystyle \frac{\pm 2}{2}} \\ {q}_{1,2}=\pm 1 \\ {q}_1=1 \\ {q}_2=-1 \\ \text{ Factored form of the equation: } \\ (q-1)(q+1)=0 \\ x\mathrm{\ne }{k}_1,k_1,q_1,q_2 \\ x\mathrm{\ne }+1;x\mathrm{\ne }-1 \\ {\displaystyle \frac{x}{x^2-2x+1}}-{\displaystyle \frac{x+3}{x^2-1}}=0 \\ {\displaystyle \frac{x}{(x-1)(x-1)}}-{\displaystyle \frac{x+3}{(x+1)(x-1)}}=0 \\ {\displaystyle \frac{x}{(x-1)}}-{\displaystyle \frac{x+3}{(x+1)}}=0 \\ x\cdot (x+1)-(x+3)\cdot (x-1)=0 \\ x=3 \\ \text{ Verifying Solution: } \\ T={\displaystyle \frac{x}{x^2-2x+1}}-{\displaystyle \frac{x+3}{x^2-1}}={\displaystyle \frac{3}{3^2-2\cdot 3+1}}-{\displaystyle \frac{3+3}{3^2-1}}=0 \end{gathered}$$

Our quadratic equation calculator calculates it.

Try another example

Showing 0 comments:

Next similar math problems:

• Eq2 2
  Solve following equation with quadratic members and rational function: (x²+1)/(x-4) + (x²-1)/(x+3) = 23
• VCP equation
  Solve the following equation with variations, combinations and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0
• Prove
  Prove that k1 and k2 is the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x²+y²+2x+4y+1=0 k2: x²+y²-8x+6y+9=0
• Intersections 3
  Find the intersections of the circles x² + y² + 6 x - 10 y + 9 = 0 and x² + y² + 18 x + 4 y + 21 = 0
• Domains of functions
  F(x)=x²-7x and g(x)=5-x² Domain of (fg)(x) is. .. . . Domain of (f/g)(x). ..
• Simple equation 6
  Solve equation with one variable: X/2+X/3+X/4=X+4
• Quadratic equation
  Find the roots of the quadratic equation: 3x²-4x + (-4) = 0.
• Linear system
  Solve a set of two equations of two unknowns: 1.5x+1.2y=0.6 0.8x-0.2y=2
• Find the 20
  Find the product and the sum of the roots of x² + 3x - 9 = 0
• Sphere equation
  Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).
• Trapezium
  The lengths of a parallel sides of a trapezium are (2x+3) and (x+8) and the distance between them is (x+4). if the area of the trapezium is 590 , find the value of x.
• Curve and line
  The equation of a curve C is y=2x² -8x+9 and the equation of a line L is x+ y=3 (1) Find the x co-ordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
• Quadratic function 2
  Which of the points belong function f:y= 2x²- 3x + 1 : A(-2, 15) B (3,10) C (1,4)
• Square root 2
  If the square root of 3m² +22 and -x = 0, and x=7, what is m?
• Perpendicular projection
  Determine the distance of a point B[1, -3] from the perpendicular projection of a point A[3, -2] on a straight line 2 x + y + 1 = 0.
• Sphere from tree points
  Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
• Quadratic equation
  Solve quadratic equation: 2x²-58x+396=0