NCTB Class 7 Math Chapter six Exercise 6.2 Solution by Math Expert. Bangladesh Board Class 7 Math Solution Chapter 6.2“Algebraic Fractions” Exercise 6.2 Solution.

Board | NCTB |

Class | 7 |

Subject | Math |

Chapter | Six |

Chapter Name | “Algebraic Fractions” |

Exercise | 6.2Solution |

__Exercise:- 6.2__

__Exercise:- 6.2__

**(1) Solution:-** 2/3a, 3/5ab

=>2/3a= 2x5b/3ax5b = 10b/15ab

= 3/5ab = 3×3/5abx3 = 9/15ab

**(2) Solution:-** x/y z, y/z x

Therefore, x/y z= x Xx/y z x x = x^{2}/x y z

y/z x = y x y/z x X y = y^{2}/x y z

**(3) Solution:-** 1/a +b + 1/a-b

= a-b +a +b/(a-b) (a-b)

(c) = 2a/a^{2}-b^{2}

**(4) Solution:-** x/2+1= 3

=> x/2 = 3-1

=> x= 4

**(5) Solution:-** a/b = a x c/b x c = ac/b c

**(6) Solution:-** 4a^{2} b- 9b^{3}/4a^{2} b +6ab^{2}

= b (2a=3b) (2a-3b)/2ab (2a+3b)

= b(2a-3b)/2ab

**(7) Solution:-** a/x+ b/x – c/x

= a +b-c/x

**(8) Solution:-** (a) (x+2) (x-2)

**(9) Solution:-** x^{2}+4x+4/x^{2}-4

= x^{2}+2. X.2+4/(x+2) (x-2)

= (x+2)^{2}/(x+2) (x-2)

= (x+2)^{2}/(x+2) (x-2)

= X+2/x-2

**(10) Solution:-** 3a/5 + 2b/5 = 3a+2b/5

** (11) Solution:-** 1/5x+ 2/5x

= 1+2/5x

= 3/5x

**(12) Solution:-** x/2z + y/3b

= 3bx+2ay/6ab

**(13) Solution:-** 2a/x+1 + 2a/x-2

= 2a(x-2) + 2a(x+1)/(x+1) (x-2)

= 4ax-4a+2a/(x+) (x-2)

= 4ax-2a/(x+1) (x-2)

= 2a(x-1)/(x+1) (x-2)

**(14) Solution:-** a/a+2 + 2/a-2

= a (a-2) + 2(a+2)/(a+2) (a-2)

= a^{2}-2a+2a+4/a^{2}-4

= a^{2}+4/a^{2} – 4

**(15) Solution:-** 3/x^{2}-4x-5 + 4/x+1

= 3/x^{2}-5x+x-5 + 4/x+1

= 3/x(x-5) (x+1) + 4/x+1

= 3+ 49x-5)/(x-1) (x-5)

= 3+ 4x-20/(x+1) (x-5)

= 4x-17/(x+1) (x-5)

**(16) Solution:-** 2a/7 – 4b/7

= 2a-4b/7

**(17) Solution:-** 2x/5a – 4y/5a

= 2x-4y/ 5a

**(18) Solution:-** a/8x- b/4y

= ay-2bx/8xy

**(19) Solution:- **3/x+3- 2/x+2

= 3(x+2) -2(x+3)/(x+3) (x+2)

= 3x+6 -2x-6/(x+3) (x+2)

= x/(x+3) (x+2)

**(20) Solution:-** p + q/p q – q + r/q r

= p r + q r-p q-p r/p q r

= q(r-p)/p q r

= (r-p)/p r

**(22) Solution:-** 5/a^{2}+6a+5 = 1/(a-1)

= 5/(a-1) (a-b) + 1/(a-1)

= 5+11 (a-5)/(a-1) (a-5)

= 5+ a-5/(a-1) (a-5)

= a/(a-1) (a-5)

**(23) Solution:-** 1/x+2 – 1/x^{2}-4

= 1/x+2 – 1/(x+2) (x-2)

= x-2 – 1/(x+2) (x-2)

= x-3/x^{2}-4

**(24) Solution:-** a/3 + a/6 -3a/8

= 8a+4a-9a/24

= 3a/24

= a/8

**(25) Solution:- **a/b – 3a/2b+ 2a/3b

= 6a-9a+4a/6b

= a/6b

**(26) Solution:- **x/y z – y/z x +z/x y

= x^{2}-y^{2}+z^{2}/x y z

**(27) Solution:- **x-y/x y + y-z/y z + z-x/z x

= z x-y z+ x y-x z +y z-x y/ x y z

= 2/ x y z

= 0

**(28) Solution:-** **(a)** x^{2}– 3xy – 4y^{2}

= x^{2}– 4xy + x y – 4y^{2}

= x(x-4y) +y(x-4y)

= (x +y) (x-4y)

**(b) Solution:- **x/x +y , x/x-4y

= L.C.M of denominator= (x+ y) (x-4y)

=> x/x +y = x X(x-4y)/ (x+ y) (x-4y) = x(x-4y)/ (x-y) (x-4y)

=> x/x-4y = x X(x +y) /(x +y) (x-4y) = x(x +y)/(x +y) (x-4y)

**(c) Solution:- **x/x +y + x/x-4y + y/x^{2}-3xy-4y^{2}

= x/ x +y + x/x-4y + y/(x +y) (x-4y)

= x^{2}– 4xy + x^{2}+ x y +y/ (x +y) (x- 4y)

= 2x^{2 }– 3x y +y/ (x +y) (x-4y)

**(29) Solution:-** A= 1/x^{2}+3x , B= 2/x^{2}+5x+6

C= 3/x^{2}– x-12

**(a) Solution:-** x^{2}=5x+6

= x^{2}+3x+2x+6

= x(x+3) +2(x+3)

= (x+3) (x+2)

**(b) Solution:-** x^{2} + 3x = X(x+3)

X^{2}+ 5x+6 = (x=3) (x+2)

X^{2}– x-12 = x^{2}-4x+3x-12

= x(x-4) +3(x-4)

= (x+3) (x-4)

Therefore, L.C.M of denominator= x(x+2) (x+3) (x-4)

Let, A= 1/x^{2}+3x

= 1x (x+2) (x-2)/x((x+3) x (x+2) (c-4)

= (x+2) (x-4)/x(x+2) (x+3) (x-4)

B= 2/x^{2}+5x+6

=2/(x+2) (x+3)

= 2x(x-4) x/(x+2) (x+3) X x(x-4)

= 2x(x-4)/x(x+2) (x+3) (x-4)

C= 3/x^{2}-x-12

= 3/(x+3) (x-4)

= 3Xx(x+2)/(x+3) (x-4) Xx(x+2)

= 3x(x+2)/x(x+2) (x+3) (x-4)

**(c) Solution:-**A+B-c

= (x+2) (x-4)/x(x+2) (x+3) (x-4) + 2x(x-4)/x(x+2) (x+3) (x-4) -3x(x+2) / x(x+2) (x+3) (x-4)

= x^{2} -4x+2x-8 +2×2-8+2x^{2}-8x-3x^{2}-6x/x(x+2) (x+3) (x-4)

= 3x^{2}-3x^{2}-18x+2x-8/x(x+2) (x+3) (x-4)

= -8-16x/x(x+2) (x+3) (x-4)

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