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Pertanyaan

Diketahui persamaan fraction numerator x minus 1 plus begin display style fraction numerator 2 over denominator x plus 2 end fraction end style over denominator x plus 1 minus begin display style fraction numerator 2 over denominator x plus 2 end fraction end style end fraction equals fraction numerator x plus m over denominator x plus n end fraction. Hitung nilai m dan n!

Y. Herlanda

Master Teacher

Mahasiswa/Alumni STKIP PGRI Jombang

Jawaban terverifikasi

Jawaban

nilai  m equals 1 comma space n equals negative 1.

Pembahasan

Operasi hitung campuran pada pecahan bentuk aljabar

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator x minus 1 plus begin display style fraction numerator 2 over denominator x plus 2 end fraction end style over denominator x plus 1 minus begin display style fraction numerator 2 over denominator x plus 2 end fraction end style end fraction end cell equals cell fraction numerator x plus m over denominator x plus n end fraction end cell row cell open parentheses x minus 1 plus fraction numerator 2 over denominator x plus 2 end fraction close parentheses divided by open parentheses x plus 1 minus fraction numerator 2 over denominator x plus 2 end fraction close parentheses end cell equals cell fraction numerator x plus m over denominator x plus n end fraction end cell row cell open square brackets fraction numerator open parentheses x plus 2 close parentheses open parentheses x minus 1 close parentheses plus 2 over denominator open parentheses x plus 2 close parentheses end fraction close square brackets divided by open square brackets fraction numerator open parentheses x plus 2 close parentheses open parentheses x plus 1 close parentheses minus 2 over denominator open parentheses x plus 2 close parentheses end fraction close square brackets end cell equals cell fraction numerator x plus m over denominator x plus n end fraction end cell row cell open square brackets fraction numerator down diagonal strike open parentheses x plus 2 close parentheses end strike open parentheses x minus 1 close parentheses plus 2 over denominator up diagonal strike open parentheses x plus 2 close parentheses end strike end fraction close square brackets cross times open square brackets fraction numerator up diagonal strike open parentheses x plus 2 close parentheses end strike over denominator down diagonal strike open parentheses x plus 2 close parentheses end strike open parentheses x plus 1 close parentheses minus 2 end fraction close square brackets end cell equals cell fraction numerator x plus m over denominator x plus n end fraction end cell row cell fraction numerator x minus 1 plus 2 over denominator x plus 1 minus 2 end fraction end cell equals cell fraction numerator x plus m over denominator x plus n end fraction end cell row cell fraction numerator x plus 1 over denominator x minus 1 end fraction end cell equals cell fraction numerator x plus m over denominator x plus n end fraction end cell end table 

Menentukan nilai m dan n

table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 1 end cell equals cell x plus m end cell row cell x minus x plus 1 end cell equals m row 1 equals m row cell x minus 1 end cell equals cell x plus n end cell row cell x minus x minus 1 end cell equals n row cell negative 1 end cell equals n end table 

Jadi, nilai  m equals 1 comma space n equals negative 1.

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