Solve the following quadratic equations by factorization method: \frac{x+3}{x-2}-\frac{1-x}{x}=\frac{17}{4}.

shelbs624c

shelbs624c

Answered question

2021-12-04

Solve the following quadratic equations by factorization method:
x+3x21xx=174.

Answer & Explanation

Donald Proulx

Donald Proulx

Beginner2021-12-05Added 18 answers

Step 1
The quadratic equation is given by
x+3x21xx=174.
To evaluate : The solution of the quadratic equation by factorization method.
Step 2
The quadratic equation can be further simplified and solved by factorization method as following :
x+3x21xx=174.
(x+3)x(1x)(x2)(x2)x=174
(x2+3x)(x2+3x2)(x22x)=174
x2+3x+x23x+2(x22x)=174
4(2x2+2)=17(x22x)
8x2+8=17x234x
9x234x8=0
9x236x+2x8=0
9x(x4)+2(x4)=0
(9x+2)(x4)=0
(9x+2)=0 or (x-4)=0
x=29 or x=4
Step 3
Hence, the solutions of the quadratic equation are : x=29 or x=4

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