Selesaikan setiap pertidaksamaan berikut. b. x−1x+1>1

Pertanyaan

Selesaikan setiap pertidaksamaan berikut.

b. $square root of fraction numerator x plus 1 over denominator x minus 1 end fraction end root greater than 1$

I. Sutiawan

Master Teacher

Mahasiswa/Alumni Universitas Pasundan

Jawaban terverifikasi

Jawaban

penyelesaian pertidaksamaan $square root of fraction numerator x plus 1 over denominator x minus 1 end fraction end root greater than 1$ adalah x greater than 1

Pembahasan

Syarat:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator x plus 1 over denominator x minus 1 end fraction end cell greater or equal than 0 end table$

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 1 end cell not equal to 0 row x not equal to cell 1 space.... space left parenthesis 2 right parenthesis end cell end table

Untuk menyelesaikan pertidaksamaan $square root of fraction numerator x plus 1 over denominator x minus 1 end fraction end root greater than 1$ kuadrat kedua ruas, sehingga:

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of fraction numerator x plus 1 over denominator x minus 1 end fraction end root close parentheses squared end cell greater than cell 1 squared end cell row cell fraction numerator x plus 1 over denominator x minus 1 end fraction end cell greater than 1 row cell fraction numerator x plus 1 over denominator x minus 1 end fraction minus 1 end cell greater than 0 row cell fraction numerator x plus 1 minus left parenthesis x minus 1 right parenthesis over denominator x minus 1 end fraction end cell greater than 0 row cell fraction numerator x plus 1 minus x plus 1 over denominator x minus 1 end fraction end cell greater than 0 row cell fraction numerator 2 over denominator x minus 1 end fraction end cell greater than 0 row x greater than cell 1 space.... space left parenthesis 3 right parenthesis end cell end table$

Iriskan (1), (2) dan (3) sehingga penyelesaian menjadi x greater than 1 .

Jadi, penyelesaian pertidaksamaan $square root of fraction numerator x plus 1 over denominator x minus 1 end fraction end root greater than 1$ adalah