Question

1/x-1 - 1/x+5 =6/7. solve the following quadratic equations by factorization.​

Answer 1

Answer:

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Answer 2

Given:-

→Equation:-

→ $\frac{1}{x-1}$-$\frac{1}{x+5}$=$\frac{6}{7}$

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To Find:-

→The Value of x, By factorization or Spiliting the Middle term?

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AnsWer:-

•Cross Multiply LHS•

→$\frac{x+5-(x-1)}{(x-1)×(x+5)}$=$\frac{6}{7}$

♦On expanding LHS♦

→$\frac{x+5-x+1}{x^{2}-x+5x-5}$=$\frac{6}{7}$

→$\frac{6}{x^{2}+4x-5}$=$\frac{6}{7}$

♦Cross Multiply LHS and RHS♦

→6(x²+4x-5)=7×6 *

→x²+4x-5=$\frac{\cancel{42}}{\cancel{6}}$

→x²+4x-5=7

→x²+4x-5-7=0

→x²+4x-12=0

๛S=4[Sum of Equation]

๛P=-12[Product of Equation]

•6-2=4=S

•6×-2=-12=P

→ x²+6x-2x-12=0

→x(x+6)-2(x+6)=0

๛x-2=0

๛x+6=0

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•Taking x-2=0

♦x=2

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•Taking x+6=0

♦x=-6

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* was put to make you understand that we can multiply 6 with the equation and get the Same Results, But that step would Decrease the calculation required

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