- Chapter 1- Rational and Irrational Numbers
- Chapter 2- Compound Interest [Without Using Formula
- Chapter 3- Compound Interest [Using Formula
- Chapter 4- Expansions
- Chapter 5- Factorisation
- Chapter 6- Simultaneous Equations
- Chapter 7- Indices [exponents]
- Chapter 8- Logarithms
- Chapter 9- Triangles [Congruency in Triangles]
- Chapter 10- Isosceles Triangle
- Chapter 11- Inequalities
- Chapter 12- Mid-Point and Its Converse
- Chapter 13- Pythagoras Theorem
- Chapter 14- Rectilinear Figures
- Chapter 15- Construction of Polygons
- Chapter 16- Area Theorems
- Chapter 17- Circles
- Chapter 18- Statistics
- Chapter 19- Mean and Median
- Chapter 20- Area and Perimeter of Plane Figures
- Chapter 21- Solids
- Chapter 22- Trigonometrical Ratios
- Chapter 23- Trigonometrical Ratios of Standard Angles
- Chapter 24- Solution Of Right Triangles
- Chapter 25- Complementary angles
- Chapter 26- Co-ordinate Geometry
- Chapter 27- Graphical Solution
- Chapter 28- Distance Formula
Selina Solutions Class 9 Mathematics Solutions for Exercise 1(D) in Chapter 1 - Chapter 1- Rational and Irrational Numbers
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Simplify:
\frac{\sqrt{x^{2}+y^{2}}-y}{x-\sqrt{x^{2}-y^{2}}} \div \frac{\sqrt{x^{2}-y^{2}}+x}{\sqrt{x^{2}+y^{2}}+y}
\begin{aligned} &\begin{aligned} & \frac{\sqrt{x^{2}+y^{2}}-y}{x-\sqrt{x^{2}-y^{2}}} \div \frac{\sqrt{x^{2}-y^{2}}+x}{\sqrt{x^{2}+y^{2}}+y} \\ =& \frac{\sqrt{x^{2}+y^{2}-y}}{x-\sqrt{x^{2}-y^{2}}} \times \frac{\sqrt{x^{2}+y^{2}}+y}{\sqrt{x^{2}-y^{2}}+x} \\ -\frac{\sqrt{x^{2}+y^{2}-y}}{x-\sqrt{x^{2}-y^{2}}} \times \frac{\sqrt{x^{2}+y^{2}+y}}{x+\sqrt{x^{2}-y^{2}}} \end{aligned}\\ &\text { Using the identify }\\ &(a+b)(a-b)=a^{2}-b^{2}\\ &\begin{array}{l} \text { we get. } \\ \qquad \begin{array}{l} \left(\sqrt{x^{2}+y^{2}}\right)^{2}-y^{2} \\ x^{2}-\left(\sqrt{x^{2}-y^{2}}\right)^{2} \\ x^{2}+y^{2}-y^{2} \\ \frac{x^{2}}{x^{2}}-x^{2}+y^{2} \\ =\frac{x^{2}}{y^{2}} \end{array} \end{array} \end{aligned}
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