Solve the following quadratic equations by factorization method: \frac{x}{x+1}+\frac{x+1}{x}=\frac{34}{15}, x\ne 0,

Krzychau1

Krzychau1

Answered question

2021-12-18

Solve the following quadratic equations by factorization method:
xx+1+x+1x=3415,x0,x1.

Answer & Explanation

Jonathan Burroughs

Jonathan Burroughs

Beginner2021-12-19Added 37 answers

Step 1
x(x+1)+x+1x=3415
x2+(x+1)2x(x+1)=3415
Step 2
15(x2+(x+1)2)=34(x(x+1))
15x2+15(x+1)2=34x2+34x
15x2+15(x2+2x+1)=34x2+34x
15x2+15x2+30x+15=34x2+34x
34x230x2+34x30x15=0
4x2+4x15=0
4x2+10x6x15=0
2x(2x+5)-3(2x+5)=0
(2x-3)(2x+5)=0
2x-3=0, 2x+5=0
x=32,x=52
x=32,52
psor32

psor32

Beginner2021-12-20Added 33 answers

Step 1
To solve the give equation
Step 2
given that the equation
xx+1+x+1x=3415
Least common multiplier of (x+1), x and 15
Multiply by LCM=15x(x+1)
xx+115x(x+1)+x+1x15x(x+1)=341515x(x+1)
15x2+15(x+1)2=34x(x+1)
30x2+30x+15=34x2+34x
30x24x+15=34x2
4x24x+15=0
-(2x-3)(2x+5)=0
x=32,x=52
nick1337

nick1337

Expert2021-12-28Added 777 answers

xx+1+x+1x=3415x2+(x+1)2x(x+1)=3415x2+x2+1+2xx2+x=34152x2+2x+1x2+x=341534x2+34x=30x2+30x+154x2+4x15=04x2+10x6x15=0
2x(2x+5)3(2x+5)=0
(2x+5)(2x3)=0
2x=-5 and 2x=3
Step 2
x=52,x=32

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