Question
Show that:
$\frac{1}{1+\text{x}^{\text{a}+\text{b}}}+\frac{1}{1+\text{x}^{\text{b}-\text{c}}}=1$
✓
Answer
$\text{LHS}=-\frac{1}{1+\text{x}^{\text{a}+\text{b}}}+\frac{1}{1+\text{x}^{\text{b}-\text{c}}}=1$
Multiplying the numerators and denominators of two terms on L.H.S.
by xb and xa respectively, we obtain
$\text{LHS}=\frac{\text{x}^\text{b}}{\text{x}^\text{b}+\text{x}^{\text{a}-\text{b}+\text{b}}}+\frac{\text{x}^\text{a}}{\text{x}^{\text{a}}+\text{x}^{\text{b}-\text{a}+\text{a}}}$
$=\frac{\text{x}^\text{b}}{\text{x}^\text{b}+\text{x}^\text{a}}+\frac{\text{x}^\text{a}}{\text{x}^\text{a}+\text{x}^\text{b}}$
$=\frac{\text{x}^\text{b}+\text{x}^\text{a}}{\text{x}^\text{b}+\text{x}^\text{a}}$
$=1$
$=\text{RHS}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the surface area of a sphere of radius 14cm.
Find theangle which is five times its supplement.
Define the following terms:
Ray.
Ray.
Factorise:
$\text{x}^2+6\sqrt{6}\text{x}+48$
→$\text{x}^2+6\sqrt{6}\text{x}+48$
Factorise:
x2 + 20x - 69
x2 + 20x - 69
Write the following in decimal form and say what kind of decimal expansion has.
$\frac{261}{400}$
→$\frac{261}{400}$
ABC is a right-angled triangle in which $\angle $A = ${90^ \circ }$ and AB = AC. Find $\angle $B and $\angle $C.
→Can a triangle have:
Two obtuse angles?
Justify your answer in case.
Two obtuse angles?
Justify your answer in case.
In Fig.,if PQ || RS, $\angle$MXQ = 135° and $\angle$MYR = 40°, find $\angle$XMY.
→Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base and two parallels:
